Chapter 5 Extra Practice Answers

1. An airline estimates that the probability that a random call to their reservation phone line result in a reservation being made is 0.31. This can be expressed as P(call results in reservation) = 0.31. Assume each call is independent of other calls. a) Describe what the Law of Large Numbers says in the context of this probability.

As the number of calls becomes larger and larger, the proportion of calls resulting in a reservation will get closer and closer to 0.31.

b) What is the probability that none of the next four calls results in a reservation?

P(four non-reservation calls) = (0.69)4 ≈ 0.2267.

c) You want to estimate the probability that exactly one of the next four calls result in a reservation being made. Assign the digits 01 through 31 to calls that result in a reservation being made and 32 through 00 to other calls. Choose four two-digit numbers from the random digits table and determine how many of the four calls result in reservations being made. The proportion of those trials that result in one call resulting in a reservation is the probability estimate. Carry out 5 trials of this simulation and estimate the probability. Mark on or above each line of the table so that someone can clearly follow your method.  

188 87370 88099 89695 87633 76987 85503 26257 51736

 

Let R = reservation made and O = other call. Starting on line 188, the first five trials are: OORO = 1 call; OOOO = no calls; OOOO = no calls; OORR = 2 calls; RORO = 2 calls.

Probability estimate is 1/5 = 0.20.Trial 1: STrial 2: FTrial 3: FTrial 4: FTrial 5: F 

2. A grocery store examines its shoppers’ product selection and calculates the following: The probability that a randomly-chosen shopper buys apples is 0.21, that the shopper buys potato chips is 0.36, and that the shopper buys both apples and potato chips is 0.09.

a) Let A = Randomly-chosen shopper buys apples, and C = Randomly-chosen shopper buys potato chips. Sketch a Venn diagram that summarizes the probabilities above.

0.12 0.09 0.27

A C

0.52

Buys Potato Chips?

Buys Apples?

Yes No

Yes 9 27

No 12 52

b) Let A = Randomly-chosen shopper buys apples, and C = Randomly-chosen shopper buys potato chips. If 100 customers visit the store today, make a two-way table that summarizes the probabilities above.

c) Find each of the following: i. The probability that a randomly-selected shopper buys apples or potato chips.

i. P(A U C) = 0.48.

ii. The probability that a randomly-selected shopper buys potato chips or doesn’t buy apples.

ii. P( AC U C) = 0.88

iii. The probability that a randomly-selected shopper doesn’t buy apples and doesn’t buy potato chips.

iii. P(AC ∩ CC) = 0.52

3. Wile E. Coyote is pursuing the Road Runner across Great Britain toward Scotland. The Road Runner chooses his route randomly, such that there is a probability of 0.8 that he’ll take the high road and 0.2 that he’ll take the low road. If he takes the high road, the probability that Wile E. catches him is 0.01. If he takes the low road, the probability he gets caught is 0.05. Find the probability that he took the high road, given that he was caught.

HR Caught 0.8 0.01HR | Caught 0.444

Caught 0.8 0.01 0.2 0.05

PP

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