Practice Questions

1. A box contains 3 yellow, 2 red, 4 green and 3 black marbles. Two marbles are taken one after the other at random from the box. What is the probability that both marbles are red?

a) 1/50

b) 1/60

c) 1/66

d) 2/57

e) 1/6

2. Four children are asked to pick their favorite ice cream flavor out of 8 different flavors, and each of them is equally likely to pick any of the eight ice cream flavors. What is the probability that each child orders a different ice cream type?

a) 100/149

b) 27/89

c) 63/128

d) 105/256

e) 66/97

3. Six fruit baskets contain peaches, apples and oranges. Three of the baskets contain two apples and one orange each, two other baskets contain three apples and one peach each, and the last basket contains two peaches and two oranges. You select a basket at random and then select a fruit at random from the basket. Which of the following is the probability that the fruit is an apple?

a) .32

b) .4

c) .46

d) .5

e) .58

4. A real estate agent finds home buyers and closes the sales for 70% of his clients that sell their homes. What is the mean number of sales for his next 10 clients and what is the standard deviation of this distribution?

a) μ = 7 and σ = 1.45

b) μ = 7 and σ = 1.5

c) μ = 7 and σ = 1.2

d) μ = 7 and σ = 0

e) μ = 7 and σ = .66

5. A box contains 3 yellow, 2 red, 4 green and 3 black marbles. Two marbles are taken one after the other at random from the box. What is the probability that both marbles are red?

a) 1/50

b) 1/60

c) 1/66

d) 1/24

e) 1/18

Free Response:

1. A media company plans to publish a special edition of a newspaper. Past experience shows that the number of newspapers the company will sell is described by the following table:

a) What is the probability that the company will sell less than 250,000 newspapers?

b) The cost of selling this special edition is $100,000 for up to 260,000 newspapers and a flat cost of $10,000 if more are sold. What is the expected sum the company will spend to sell the special edition?

c) Given that the company spends the flat extra cost of $10,000, what is the probability that the company sells between $270,000 and $280,000 newspapers?

2. If you draw an M&M candy at random from a bag of the candies, the candy you draw will have one of six colors. The probability of drawing each color depends on the proportion of each color among all candies made.

(a) The table below gives the probability of each color for a randomly chosen plain M&M:

Color: Brown Red Yellow Green Orange Blue

Probability 0.3 0.2 0.2 0 .1 0.1 ?

What must be the probability of drawing a blue candy?

.

(b) The probability for peanut M&Ms are a bit different. Here they are

Color: Brown Red Yellow Green Orange Blue

Probability: 0.2 0.1 0.2 0.1 0.1 ?

What is the probability that a peanut M&M chosen at random is blue?

(c) What is the probability that a plain M&M is any of red, yellow, or orange? What is the probability that a peanut M&M has one of these colors?

3. A string of Christmas lights contains 20 lights. The lights are wired in series, so that if any light fails the whole string will go dark. Each light has probability 0.02 of failing during a 3-year period. The lights fail independently of each other. What is the probability that the string of lights will remain bright for 3 years?

Solutions: