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Year 10 Mathematics
Probability Test
(70 minutes)
Calculator permitted
Name: _____________________
Part 1 Multiple Choice Questions 1 0 marks
Circle the letter corresponding to the correct answer.
- A letter is chosen at random from the word CEREMONY. The probability that the letter is an E is:
A.
B.
C.
D.
E.
- 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:
A.
p q
q −
B. q
C.
p q
p
D. p q
q
E. q
p
Mark: /
- 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.
B. 0.
C. 0.
D. 0.
E. 0.
Number of heads 0 1 2 3 Frequency 15 20 29 36
- 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
- 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.
- The probability that a randomly chosen student from the class likes horror movies but not comedy movies is:
A.
B.
C.
D.
E.
A B
C H
Part 2 Short Answer Questions 25 marks
Show relevant working throughout.
- 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
- 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 0 – 3 4 – 7 8 or more Frequency 64 12 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
- 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.
×
Blue Die 1 2 3 4
Red Die
(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
- 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 ′)
1 + 1 = 2 marks
- (a) Shade the stated region on the following Venn diagrams.
i. A ∩ B ii. A ′ ∪ B ′
(b) Hence, if Pr( A ∩ B ) = 0.3, what is Pr( A ′ ∪ B ′)?
(1 + 1) + 1 = 3 marks
A B^ A^ B
Part 3 Extended Response Questions 15 marks
Planning is under way for the upcoming Community Day Fair.
- At last year’s Fair, a number of people were surveyed as to whether or not they purchased hot chips ( C ) or a drink ( D ) at the Fair. The survey data is summarised in the Venn diagram below.
(a) Use the Venn diagram to determine: i. Pr( D ) ii. Pr( D | C )
1 + 2 = 3 marks
(b) Based on the data provided, are the events D and C independent? Why/why not? Give a mathematical reason.
2 marks
Please turn over for the next question
C D
- A number of games are also being planned for the Fair.
(a) One of the games involves a lucky dip for young children where there are three buckets to choose from containing a mixture of yo-yos ( Y ) and stress balls ( S ) (they are in the same size packaging so that you can’t tell them apart).
In bucket A there are 2 yo-yos and 3 stress balls. Bucket B contains 7 stress balls and no yo-yos. Bucket C contains 5 yo-yos and 5 stress balls.
A young girl randomly chooses a bucket and then randomly chooses a toy from that bucket.
i. What is the probability that she chose bucket A?
1 mark ii. Complete the tree diagram below, showing the selection of a bucket and the selection of a toy, by labelling each branch with its associated probability.
2 marks iii. What is the probability that she selected a yo-yo (from any bucket)?
2 marks
It turns out the young girl did select a yo-yo.
iv. Given this knowledge, what is the probability the yo-yo came from bucket A?
2 marks
A
B
C
Y
S
Y
Y
S
S
