Probability Practice Test Questions! Quiz

1) A number is chosen at random from set S = {3, 5, 9, 12, 16, 25, 27, 29}. Find the probability that the number chosen is a perfect square.

3/8

1/2

3/4

5/8

The set S contains 8 numbers. Out of these, the perfect squares are 3, 9, 16, and 25. So, there are 4 perfect squares in the set. The probability of choosing a perfect square is the number of favorable outcomes (4) divided by the total number of possible outcomes (8). Therefore, the probability is 4/8, which simplifies to 1/2.

Explanation

The set S contains 8 numbers. Out of these, the perfect squares are 3, 9, 16, and 25. So, there are 4 perfect squares in the set. The probability of choosing a perfect square is the number of favorable outcomes (4) divided by the total number of possible outcomes (8). Therefore, the probability is 4/8, which simplifies to 1/2.

2) A bag contains 8 red beads, 14 green beads and x blue beads. If a bead is picked at random from the bag, the probability of picking a green bead is 1/3. Find the value of x.

20

22

23

25

If the probability of picking a green bead is 1/3, it means that out of the total number of beads in the bag, 1/3 of them are green. We know that there are 8 red beads and 14 green beads in the bag, so the total number of beads in the bag is 8 + 14 + x. Therefore, we can set up the equation (14 / (8 + 14 + x)) = 1/3. Solving this equation, we find that x = 20.

Explanation

If the probability of picking a green bead is 1/3, it means that out of the total number of beads in the bag, 1/3 of them are green. We know that there are 8 red beads and 14 green beads in the bag, so the total number of beads in the bag is 8 + 14 + x. Therefore, we can set up the equation (14 / (8 + 14 + x)) = 1/3. Solving this equation, we find that x = 20.

3) A container contains sweets of orange, coffee and pineapple flavours. A child picks one sweet at random from the container. The probabilities of him choosing a sweet with an orange flavour and a sweet with a coffee flavour are 2/9 and 1/3 respectively. If the number of sweets with pineapple flavour is 160, find the total number of sweets in the container.

450

360

315

270

Let's assume the total number of sweets in the container is x. We are given that the probability of choosing a sweet with an orange flavor is 2/9, which means there are 2x/9 orange flavored sweets. Similarly, the probability of choosing a sweet with a coffee flavor is 1/3, which means there are x/3 coffee flavored sweets. We are also given that there are 160 pineapple flavored sweets. Therefore, the total number of sweets can be calculated by adding the number of orange, coffee, and pineapple flavored sweets: 2x/9 + x/3 + 160 = x. Simplifying this equation, we get x = 360. Therefore, the total number of sweets in the container is 360.

Explanation

Let's assume the total number of sweets in the container is x. We are given that the probability of choosing a sweet with an orange flavor is 2/9, which means there are 2x/9 orange flavored sweets. Similarly, the probability of choosing a sweet with a coffee flavor is 1/3, which means there are x/3 coffee flavored sweets. We are also given that there are 160 pineapple flavored sweets. Therefore, the total number of sweets can be calculated by adding the number of orange, coffee, and pineapple flavored sweets: 2x/9 + x/3 + 160 = x. Simplifying this equation, we get x = 360. Therefore, the total number of sweets in the container is 360.

4) There are 24 Mathematics books, 30 Science books and 36 History books in a book rack. A book is picked at random from the rack. The probability of picking a Mathematics book is

1/4

4/15

1/3

2/5

The probability of picking a Mathematics book can be calculated by dividing the number of Mathematics books by the total number of books in the rack. In this case, there are 24 Mathematics books out of a total of 24 + 30 + 36 = 90 books. Therefore, the probability of picking a Mathematics book is 24/90, which simplifies to 4/15.

Explanation

The probability of picking a Mathematics book can be calculated by dividing the number of Mathematics books by the total number of books in the rack. In this case, there are 24 Mathematics books out of a total of 24 + 30 + 36 = 90 books. Therefore, the probability of picking a Mathematics book is 24/90, which simplifies to 4/15.

5) A box contains 24 green T-shirts and some red T-shirts. A T-shirt is chosen at random from the box. The probability of choosing a green T-shirt is 3/8. Find the number of red T-shirts in the box.

25

30

35

40

The probability of choosing a green T-shirt is given as 3/8. Since there are 24 green T-shirts in the box, we can set up the equation (24)/(24 + x) = 3/8, where x represents the number of red T-shirts. By cross-multiplying and solving for x, we find that x = 40. Therefore, there are 40 red T-shirts in the box.

Explanation

The probability of choosing a green T-shirt is given as 3/8. Since there are 24 green T-shirts in the box, we can set up the equation (24)/(24 + x) = 3/8, where x represents the number of red T-shirts. By cross-multiplying and solving for x, we find that x = 40. Therefore, there are 40 red T-shirts in the box.

6) In a group, 350 of the 450 workers are female. Then 50 male workers join the group. A worker is chosen at random from the group. Find the probability of choosing a male worker.

2/9

7/9

3/10

1/10

In the group, there are initially 450 workers, with 350 of them being female. This means that there are 100 male workers in the group. After 50 male workers join, the total number of workers becomes 500, with 150 of them being male. Therefore, the probability of choosing a male worker at random from the group is 150/500, which simplifies to 3/10.

Explanation

In the group, there are initially 450 workers, with 350 of them being female. This means that there are 100 male workers in the group. After 50 male workers join, the total number of workers becomes 500, with 150 of them being male. Therefore, the probability of choosing a male worker at random from the group is 150/500, which simplifies to 3/10.

7) There are 56 red ink pens and a number of black ink pens in a box. The probability that a black ink pen is chosen at random from the box is 3/7. How many black ink pens in the box?

42

49

60

98

If the probability of choosing a black ink pen from the box is 3/7, it means that out of the total number of pens in the box, 3/7 of them are black ink pens. Since there are 56 red ink pens in the box, the remaining pens must be black ink pens. Therefore, the total number of black ink pens in the box is 3/7 times the total number of pens, which is 56 + 3/7 * (56) = 42.

Explanation

If the probability of choosing a black ink pen from the box is 3/7, it means that out of the total number of pens in the box, 3/7 of them are black ink pens. Since there are 56 red ink pens in the box, the remaining pens must be black ink pens. Therefore, the total number of black ink pens in the box is 3/7 times the total number of pens, which is 56 + 3/7 * (56) = 42.

8) A box contains with 27 Mathematics and Science books. If a book is selected at random from the box, the probability of selecting a Science book is 4/9. Then 3 Mathematics books and 2 Science books are added into the box. A book is selected at random from the box. Find the probability of selecting a Mathematics book.

15/32

17/32

5/9

9/16

After adding 3 Mathematics books and 2 Science books, the total number of books in the box becomes 27 + 3 + 2 = 32. The number of Mathematics books in the box is now 27 + 3 = 30. Therefore, the probability of selecting a Mathematics book is 30/32, which simplifies to 15/16.

Explanation

After adding 3 Mathematics books and 2 Science books, the total number of books in the box becomes 27 + 3 + 2 = 32. The number of Mathematics books in the box is now 27 + 3 = 30. Therefore, the probability of selecting a Mathematics book is 30/32, which simplifies to 15/16.

9) Faizah receives 36 Hari Raya greeting cards from overseas and 56 greeting cards sent locally. One third of the overseas cards and three quarters of the local cards are from her relatives. If Faizah picks a greeting card at random, what is the probability that the greeting card is not from her relatives?

27/46

11/12

19/46

12/13

Out of the 36 overseas cards, one third (12 cards) are from her relatives. Out of the 56 local cards, three quarters (42 cards) are from her relatives. Therefore, the total number of cards from her relatives is 12 + 42 = 54. The total number of cards is 36 + 56 = 92. The probability of picking a card that is not from her relatives is the number of cards that are not from her relatives (92 - 54 = 38) divided by the total number of cards (92), which simplifies to 19/46.

Explanation

Out of the 36 overseas cards, one third (12 cards) are from her relatives. Out of the 56 local cards, three quarters (42 cards) are from her relatives. Therefore, the total number of cards from her relatives is 12 + 42 = 54. The total number of cards is 36 + 56 = 92. The probability of picking a card that is not from her relatives is the number of cards that are not from her relatives (92 - 54 = 38) divided by the total number of cards (92), which simplifies to 19/46.

10) A basket contains 15 bottles of flavoured-orange drink and vanilla-flavoured drink. If a bottle is selected at random from the basket, the probability of selecting a bottle of orange-flavour drink is 3/5. Then five bottles of orange-flavoured drink are added into the basket. If a bottle is selected at random from the basket, find the probability of selecting a bottle of vanilla-flavour drink.

1/5

2/5

3/10

7/10

After adding five bottles of orange-flavoured drink, the total number of bottles in the basket becomes 15 + 5 = 20. Since the probability of selecting an orange-flavoured drink is 3/5, it means that there are 3/5 * 20 = 12 bottles of orange-flavoured drink in the basket. Therefore, the number of vanilla-flavoured drink bottles in the basket is 20 - 12 = 8. So, the probability of selecting a vanilla-flavoured drink is 8/20, which simplifies to 2/5.

Explanation

After adding five bottles of orange-flavoured drink, the total number of bottles in the basket becomes 15 + 5 = 20. Since the probability of selecting an orange-flavoured drink is 3/5, it means that there are 3/5 * 20 = 12 bottles of orange-flavoured drink in the basket. Therefore, the number of vanilla-flavoured drink bottles in the basket is 20 - 12 = 8. So, the probability of selecting a vanilla-flavoured drink is 8/20, which simplifies to 2/5.