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Chapter 3: Q3.10 (page 186)

A student goes to the library. Let events B = the student checks out a book and D = the student checks out a DVD. Suppose that P(B) = 0.40, P(D) = 0.30 and P(B AND D) = 0.20.

a. Find P(B|D).

b. Find P(D|B).

c. Are B and D independent?

d. Are B and D mutually exclusive?

Short Answer

Expert verified

a] P(B|D) = 0.66 ; b] P(D|B) = 0.5 ; c] No, B & D are not independent ; D] No, B & D are not mutually exclusive

Step by step solution

01

Probability 

A] P(B|D) = Pr (Student B checks out a book, given he checks out a DVD)

= P (B & D) / P (D) = P (B & D) / P (D) = 0.20 / 0.30 = 0.66

B] P(D|B) = Pr (Student B checks out a DVD, given he checks out a book)

= P (B & D) / P (B) = P (B & D) / P (B) = 0.20 / 0.40 = 0.5

02

Mutually Exclusiveness & Independence Concepts 

  • Mutually Exclusive events are those, which cannot happen simultaneously, like a coin tossed once can't get both head & tail.

As student can check out both a book & a DVD, so event B & D are not mutually exclusive.

  • Independent Events are those, whose occurrence of one event doesn't effect occurrence of other event. In case of such events, Pr (A & B) = Pr (A) x Pr (B)

As Pr (B & D) ie looking both book & DVD is not = P (B) P (D) , as 0.40 x 0.30 鈮� 0.20

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Most popular questions from this chapter

Use the following information to answer the next six exercises. There are 23countries in North America, 12countries in

South America, 47countries in Europe, 44countries in Asia, 54countries in Africa, and 14in Oceania (Pacific Ocean

region).

Let A = the event that a country is in Asia.

Let E = the event that a country is in Europe.

Let F = the event that a country is in Africa.

Let N = the event that a country is in North America.

Let O = the event that a country is in Oceania.

Let S = the event that a country is in South America.

Find P(A).

Roll a fair, six-sided die. Let A = a prime number of dots is rolled. Let B = an odd number of dots is rolled. Then A = {2, 3, 5} and B = {1, 3, 5}. Therefore, A AND B = {3, 5}. A OR B = {1, 2, 3, 5}. The sample space for rolling a fair die is S = {1, 2, 3, 4, 5, 6}. Draw a Venn diagram representing this situation.

Use the following information to answer the next three exercises. The casino game, roulette, allows the gambler to bet on the probability of a ball, which spins in the roulette wheel, landing on a particular color, number, or range of numbers. The table used to place bets contains of 38numbers, and each number is assigned to a color and a range.

a. List the sample space of the 38possible outcomes in roulette.

b. You bet on red. Find P(red).

c. You bet on -1st12- (1st Dozen). Find P1st12.

d. You bet on an even number. Find P(even number).

e. Is getting an odd number the complement of getting an even number? Why?

f. Find two mutually exclusive events.

g. Are the events Even and 1stDozen independent?

Use the following information to answer the next two exercises. You are rolling a fair, six-sided number cube. Let E = the event that it lands on an even number. Let M = the event that it lands on a multiple of three.

What does P(E OR M) mean in words?

Let event A = learning Spanish. Let event B = learning German. Then A AND B = learning Spanish and German.Suppose P(A) = 0.4 and P(B) = 0.2. P(A AND B) = 0.08. Are events A and B independent? Hint: You must show ONE of the following:

鈥� P(A|B) = P(A)

鈥� P(B|A) = P(B)

鈥� P(A AND B) = P(A)P(B)
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