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People on the street were asked "How many siblings do you have?". The following diagram shows the result:
How many people answered the question?
Explanation The diagram shows that the number of people who answered the question is 30.
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2.
People on the street were asked "How many siblings do you have?". The following diagram shows the result:
What's the mode?
Explanation "Mode" isthe most frequently occurring value.
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3.
People on the street were asked "How many siblings do you have?". The following diagram shows the result:
What's the mean?
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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4.
People on the street were asked "How many siblings do you have?". The following diagram shows the result:
What's the median?
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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5.
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?
A.
200 people is not enough - more people should be asked!
B.
There should be a random sample! People attending the theater are more interested in culture than an average citizen!
Correct Answer
B. There should be a random sample! People attending the theater are more interested in culture than an average citizen!
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.
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6.
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)
Correct Answer 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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7.
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)
Correct Answer 20/56 10/28 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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8.
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.
Correct Answer 1/10 0,10 0.10 10% 0,1 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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9.
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)
Correct Answer 6,8% 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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10.
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)
Correct Answer 1,3% 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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11.
Use the grid to determine the probability of getting the sum 7 when two dice are rolled. (Express your answer as a fraction)
Correct Answer 1/6 6/36
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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12.
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?
A.
Getting the sum 5 is more likely
B.
Getting the sum 10 is more likely
Correct Answer
A. Getting the sum 5 is more likely
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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13.
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)
Correct Answer 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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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)
Correct Answer 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.
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.)
Correct Answer 3/11
16.
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)
Correct Answer 0,8% 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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17.
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)
Correct Answer 99,2% 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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