January 9, 2021

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MDM4U8 Name: __________________________ Date: __________________

QUIZ: Probability Distributions

Instructions:

• Do not begin this paper until instructed to do so.

• Unless otherwise stated in the question, all numerical answers should be given exactly or correct

to three significant figures.

• For full marks, show all your work and use proper notation.

1. A test has five questions. To pass the test, at least three of the questions must be answered correctly.

The probability that Maya answers a question correctly is 20%. Let X be the number of questions

that Maya answers correctly.

(a) Find E(X). (1)

(b) Find the probability that Maya passes the test. (2)

2.

!!𝑃

(

𝑋 = 𝑥

)

=!

"!#$

for x = 0, 1, 2, 3 is a probability distribution function.

(a) Find k. (3)

(b) Find P(X ≥ 1). (2)

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3. A box holds 240 eggs. The probability that an egg is brown is 0.05.

(a) Find the expected number of brown eggs in the box. (1)

(b) Find the probability that there are 15 brown eggs in the box. (2)

(c) Find the probability that there are at least 10 brown eggs in the box. (3)

4. A random variable X is distributed normally with a mean of 20 and variance 9.

(a) Find P(X ≤ 24.5). (3)

(b) Let P(X ≤ k) = 0.85.

(i) Represent this information on the following diagram. (2)

(ii) Find the value of k. (3)

5. Evan likes to play two games of chance, A and B.

For game A, the probability that Evan wins is 0.9. He plays game A seven times.

(a) Find the probability that he wins exactly four games. (2)