Year 10 Mathematics Probability Test

Mark: /50

Year 10 Mathematics

Probability Test

(70 minutes) Calculator permitted

Name: _____________________

Part 1

Multiple Choice Questions

10 marks

Circle the letter corresponding to the correct answer.

1. A letter is chosen at random from the word CEREMONY. The probability that the letter is an E is:

1 A.

4 B. 1

7 2 C. 7 1 D. 8 E. 1 3

2. In a bag of red and green M&Ms there are p green M&Ms and q red M&Ms. The probability of selecting a red M&M at random from the bag is:

q A. p - q

1 B. q

p C. p + q

q D. p + q

p E. q

1

3. An experiment involves tossing three biased coins and counting the number of heads. The results after running the experiment 100 times are shown in the table below. The experimental probability of obtaining at least 2 heads is:

A. 0.36 B. 0.29 C. 0.65 D. 0.35 E. 0.49

Number of heads 0 1 2 3

Frequency

15 20 29 36

4. The shaded (grey) region in the Venn diagram shown represents the region:

A. A only B. A C. A B D. B E. A | B

A

B

5. Which of the following statements is always true for mutually exclusive events A and B?

A. Pr(A | B) = 1 B. Pr(A B) = 0 C. Pr(A) + Pr(B) = 1 D. Pr(A B) = 0 E. Pr(A) = 0

Questions 6 relates to the following information.

The Venn diagram shown displays, for a class of Year 10 students, those that like comedy movies (C), those that like horror movies (H) and those that like neither.

C

H

9 45

3

6. The probability that a randomly chosen student from the class likes horror movies but not comedy movies is:

4 A.

21 5 B. 21 C. 2 9 5 D. 18 3 E. 7

2

7. The probability that a certain competitor in an archery competition hits the target is a where 0 < a < 1. The probability that the competitor does not hit the target is:

A. 1 + a B. a ? 1

1 C.

a D. 1 ? a E. Not enough information to determine.

8. Two letters are chosen from the word HELLO without replacement. The probability of selecting two Ls is:

A. 0.16 B. 0.1 C. 0.05 D. 0.2 E. 0.4

9. A music playlist has 6 pop songs and 4 jazz songs to choose from. Assuming the same song can be played twice in a row, the probability of hearing two consecutive pop songs is:

1 A.

5 B. 3

5 C. 1

3 6 D. 25 9 E. 25

10. Given events A and B are independent and that Pr( A) = 0.7 and Pr(B) = 0.6 , then Pr(B | A) is:

A. 0.6 B. 0.3 C. 0.7 D. 0.42 E. 0.1

3

Part 2

Short Answer Questions

25 marks

Show relevant working throughout.

1. From a group of 30 people surveyed, it is found that 8 enjoy snowboarding (B) and 10 enjoy skiing (S), while 5 like both.

(a) Complete the following two-way table using this information.

B

B

S

5

S 30

(b) State n(S only).

(c) Find Pr(B S).

2 + 1 + 1 = 4 marks

2. Before boxes of chocolates are sent to the retailer they are inspected for damaged chocolates. The following data was recorded from a sample of 80 boxes.

Number damaged Frequency

0 ? 3 64

4 ? 7 12

8 or more 4

(a) Boxes are rejected if there are 4 or more damaged chocolates. Determine the probability that a randomly selected box will be rejected.

(b) From this data, out of 400 boxes how many could be expected to have between 0 and 3 damaged chocolates?

1 + 2 = 3 marks 4

3. A four-sided blue die and a four-sided red die are rolled and their product (?) is written down. (a) Complete the table to represent the outcomes of the product.

Red Die

? 1

1 2 3 3 4

Blue Die

2

3

4

6

9

12

(b) Find the probability of the dice faces multiplying to an odd number.

(c) Find the probability of the dice faces multiplying to an odd number, given that the red die showed an odd number.

1 + 1 + 2 = 4 marks

4. Two events A and B are such that Pr(A) = 0.45, Pr(B) = 0.7 and Pr(A B) = 0.35. Find:

(a) Pr(A B)

(b) Pr(A B)

5. (a) Shade the stated region on the following Venn diagrams.

i. A B

ii. A B

A

B

A

1 + 1 = 2 marks B

(b) Hence, if Pr(A B) = 0.3, what is Pr(A B)? 5

(1 + 1) + 1 = 3 marks

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