Math Quiz Statistics And Probability

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1. A culture assiciation wanted to find out what the citizens of the town thought about the idea of building a new house of culture. A survey was made and 200 people who were entering the theater were asked. Which of the following alternatives is the highest contributor to a source of error being made in this survey?

200 people is not enough - more people should be asked!

There should be a random sample! People attending the theater are more interested in culture than an average citizen!

The correct answer is "There should be a random sample! People attending the theater are more interested in culture than an average citizen!" This is because the survey was conducted by asking people who were entering the theater, which means that the sample is biased towards individuals who are already interested in culture. To get a more accurate representation of the town's opinion, a random sample should be chosen to ensure that all citizens have an equal chance of being included in the survey.

Explanation

The correct answer is "There should be a random sample! People attending the theater are more interested in culture than an average citizen!" This is because the survey was conducted by asking people who were entering the theater, which means that the sample is biased towards individuals who are already interested in culture. To get a more accurate representation of the town's opinion, a random sample should be chosen to ensure that all citizens have an equal chance of being included in the survey.

About This Quiz

Math Quiz Statistics And Probability - Quiz

This Math Quiz focuses on statistics and probability, assessing understanding of sibling counts, modes, medians, and means. It also explores error sources in surveys and sampling methods, enhancing... see morestatistical literacy and data interpretation skills. see less

2. People on the street were asked "How many siblings do you have?". The following diagram shows the result:

How many people answered the question?

The diagram shows that the number of people who answered the question is 30.

Explanation

The diagram shows that the number of people who answered the question is 30.

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3.

Use the grid to determine which event has the highest probability: getting the sum 5 or getting the sum 10 when two dice are rolled?

Getting the sum 5 is more likely

Getting the sum 10 is more likely

We can get the sum 5 in four different ways and the sum 10 in only three different ways, and therefore P(sum 5) is greater than P(sum 10)

Explanation

We can get the sum 5 in four different ways and the sum 10 in only three different ways, and therefore P(sum 5) is greater than P(sum 10)

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5. You have received a phone number on a note, but the last digit in the number is missing! 073-309601.... Determine the probability that by choosing a random number for the last digit, you will get the correct phone number.

Since there are 10 digits from 0-9 and only one is correct, the probability is 1/10 or 10% or 0,1

Explanation

Since there are 10 digits from 0-9 and only one is correct, the probability is 1/10 or 10% or 0,1

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6.

Use the grid to determine the probability of getting the sum 7 when two dice are rolled. (Express your answer as a fraction)

We can get the sum 7 in six different ways, and the total outcomes when rolling two dice are 36. Hence P(sum 7) = 6/36 = 1/6

Explanation

We can get the sum 7 in six different ways, and the total outcomes when rolling two dice are 36. Hence P(sum 7) = 6/36 = 1/6

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7. A bag of marbles contains 5 black and 3 white marbles. You pick two marbles without looking (and no replacement). Determine the probability that the first marble is black. (Express your answer as a fraction)

There are a total of 8 marbles, and 5 of them are black, hence the probability for black is 5/8.

Explanation

There are a total of 8 marbles, and 5 of them are black, hence the probability for black is 5/8.

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8. Match the following events by the correct probabilities:

To get head or tail when flipping a coin

That a grasshopper can jump to the moon

To get four aces when four cards are drawn from a full deck of cards

That a 20-year old person will turn at least 50 years old

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9. When a statistical survey is made we can have different sources of errors. Match the following options:

Measurment error

Sampling error

Non-respons

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10.

M=Male F=Female Use the tree diagram to determine the probability that a family with three children consists of three boys. (Express your answer as a fraction)

P(M)=1/2, hence P(M, M, M) = 1/2 x 1/2 x 1/2 = 1/8

Explanation

P(M)=1/2, hence P(M, M, M) = 1/2 x 1/2 x 1/2 = 1/8

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11. People on the street were asked "How many siblings do you have?". The following diagram shows the result:

What's the mean?

The mean is calculated by adding all the siblings together and then divide by the number of people participating. In this case: 0x5 + 1x15 + 2x7 + 3x2 + 4x1 = 39 and there were 30 people participating, so 39/30 = 1,3.

Explanation

The mean is calculated by adding all the siblings together and then divide by the number of people participating. In this case: 0x5 + 1x15 + 2x7 + 3x2 + 4x1 = 39 and there were 30 people participating, so 39/30 = 1,3.

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12. A bag with marbles contains 5 black and 3 white marbles. You pick two marbles without looking (and no replacement). Determine the probability that both marbles are black. (Write as a fraction)

Probability for the first marble to be black is 5/8. Since there is no replacement the probability changes for the next one to be black, which is then 4/7. Product rule is used for compound events, hence the probability for black, black is: P(black, black) = 5/8 x 4/7 = 20/56 = 5/14

Explanation

Probability for the first marble to be black is 5/8. Since there is no replacement the probability changes for the next one to be black, which is then 4/7. Product rule is used for compound events, hence the probability for black, black is: P(black, black) = 5/8 x 4/7 = 20/56 = 5/14

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13. People on the street were asked "How many siblings do you have?". The following diagram shows the result:

What's the median?

The median is the value in the middle when you order the data set from smallest number to the largest. In this case we know that we have 30 data values, so we will get two values in the middle - value nr15 and value nr16. By reading the diagram we find that value nr 15 and 16 are both the number 1, so the mean of these two values will be (1+1)/2 =1. Hence the median is 1.

Explanation

The median is the value in the middle when you order the data set from smallest number to the largest. In this case we know that we have 30 data values, so we will get two values in the middle - value nr15 and value nr16. By reading the diagram we find that value nr 15 and 16 are both the number 1, so the mean of these two values will be (1+1)/2 =1. Hence the median is 1.

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14.

M=Male F=Female Use the tree diagram to determine the probability that the children in a family with three children have different gender. (Express your answer as a fraction)

Each outcome has a probability of 1/8, and there can be different genders in 6 different ways. So P(different genders) = 6/8 = 3/4

Explanation

Each outcome has a probability of 1/8, and there can be different genders in 6 different ways. So P(different genders) = 6/8 = 3/4

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15. All students in a town were tested for colour blindness: Normal vision: Boys 9800 Girls 9360 Colour blind: Boys 720 Girls 120 a) Determine the probability that a girl is colour blind. (Express your answer in percentage form)

120 girls were colour blind and there were a total of 9480 girls. The probability is then 120/9480 = 0,0126 = 1,3%

Explanation

120 girls were colour blind and there were a total of 9480 girls. The probability is then 120/9480 = 0,0126 = 1,3%

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16. Instead of asking the whole population a sample can be made. Match the following sample methods by a corresponding example:

Exhaustive sampling

Systematical sampling

Simple random sample

Stratified sample

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17. All students in a town were tested for colour blindness: Normal vision: Boys 9800 Girls 9360 Colour blind: Boys 720 Girls 120 a) Determine the probability that a boy is colour blind. (Express your answer in percentage form with one decimal)

720 boys were colour blind and there were a total of 10520 boys.. The probability is then 720/10520 = 0,068 = 6,8%

Explanation

720 boys were colour blind and there were a total of 10520 boys.. The probability is then 720/10520 = 0,068 = 6,8%

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18. You plant three seeds. The chance for a seed to grow is 80%. Determine the probability that no seed grows. (Express your answer in percentage form)

P(one seed will not grow)=20% = 0,2
P(all three seeds will not grow) = 0,2 x 0,2 x 0,2 = 0,008 = 0,8%

Explanation

P(one seed will not grow)=20% = 0,2
P(all three seeds will not grow) = 0,2 x 0,2 x 0,2 = 0,008 = 0,8%

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19. There are 4 grey socks, 4 black socks and 4 white socks in a drawer. You pick two socks without looking (and without replacement). What are chances that both socks have the same colour? (Draw a tree diagram and then express your answer as a fraction.)

Explanation

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20. Match the following events by it's complementary event:

Getting 5 or 6 when a die is rolled

Getting at least a 3 when a die is rolled

Getting at least one 6 when two dice are rolled

Getting a maximum of one 6 when rolling two dice

The complementary event is what happens if the event doesn't happen. For example - what happens if you don't get a 5 or 6 when a die is rolled? You get a 1, 2, 3 or 4! (The outcomes who are left)

Explanation

The complementary event is what happens if the event doesn't happen. For example - what happens if you don't get a 5 or 6 when a die is rolled? You get a 1, 2, 3 or 4! (The outcomes who are left)

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21. You plant three seeds. The chance for a seed to grow is 80%. Determine the probability that at least one seed grows. (Express your answer in percentage form)

"At least one seed grows" is complementary event to "not one seed will grow".
Since P(not one seed will grow) = 0,2 x 0,2 x 0,2 = 0,008 then P(at least one seed will grow) = 1 - 0,008 = 0,992 = 99,2%

Explanation

"At least one seed grows" is complementary event to "not one seed will grow".
Since P(not one seed will grow) = 0,2 x 0,2 x 0,2 = 0,008 then P(at least one seed will grow) = 1 - 0,008 = 0,992 = 99,2%

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