## Fire Department Volunteers

The ages of the volunteer members of fire department are normally distributed with a mean of 36 and a standard deviation of 6.

What is the probability that a member selected at random will be between the ages of 33 and 45?

## Independent events

Events a and B are independent. P(A)=0.72 and P(A and B)=0.18

What is P(B) equal to?

## Wrestlers

16 wrestlers compete in a competition. If each wrestler has one match with each of the other 15 wrestlers, what is the total number of matches.

## binomial probability density function

Identify each variable in the formula for the binomial probability density function. Also, explain what the fraction: n! / (n-x)!x! calculates.

## Indiana State Shipments

In a shipment of 14 computer parts to Indiana State, 3 are faulty and the remaining 11 are in working order. Three elements (parts) are randomly chosen out of the shipment. What is the probability that all three faulty elements will be the ones chosen?

## Card Solution

Please explain why in a two card hand out of a deck of 52 cards the probability of getting 2 consecutive cards is 208/1326, how did you get this?

## Day Worker Probability

1. A group of day to day workers can work either 0 hours, eight hours or 12 hours at a pay rate of $9.75 per hour. (The 12 hour day pays regular time for the first eight hours and double time for the remaining four hours.) On any given day there is a 0.2 probability of not working at all, 0.7 probability of working an eight hour shift and a 0.1 probability of working a 12 hour shift.

a. What is the probability of working at least some of the time during a day?

b. What is the expected amount of work per day?

c. What is the variation in the expected amount of work per day?

d. What is the expected pay per day?

e. What are the expected earnings in a 5-day work week?

## Approximate of Cameras Sold

1. The camera department of a large department store sells three different brands of cameras: Proxima, Yakima, and Tetron. Approximately 60% of the cameras sold are Yakimas with Tetrons accounting for 30% of sales and Proxima the remaining 10%. Store records show that approximately ¼ of those who purchase a Yakima return within one year to purchase accessories for their camera. The corresponding figures for the other two are: Tetron, 1/5; and Proxima, 3/5. If a person is known to have purchased an accessory within a year of the purchase of a camera, what is the probability the person purchased a Yakima?

## Role of the Die

A fair die is rolled until win or loss occurs:

For k=1 to 5: if a 6 occurs on the kth roll you win N dollars and game ends; if a number<k occurs you lose $10 and the game ends; otherwise you roll again.

For k>5: if a 6 occurs on the kth roll you win N dollars and the game ends; if a number<5 occurs you lose $10 and the game ends; if a 5 occurs you roll again.

what value should N have for this game to be fair?

## Chip Probability

A bowl contains R red and W white chips. Suppose N chips are drawn without replacement from the bowl.

(a) what is the expected number of red chips among the N drawn? The expected number of white chips?

(b) Justify your answers from part(a)

## Independent Trials

Suppose a sequence of independent trials is performed where each trial results in either success or failure. Suppose X=the number of failures before the first success, with p=probability of success on any one trial.

(a) Find the expected value of X. Be sure to show in detail how you got your answer.

(b) Carefully interpret the result in (a)

## Incoming Phone Calls

A certain company relies heavily on phone orders. Suppose past records show that R% of all incoming phone calls to this company are orders from customers. At least how big must R be for you to be at least 90% sure that the first phone order of the day will occur on or before the tenth incoming call of the day?

## Binominal Distribution

A new component for an airplane is being manufactured. Each has a 70% probability of working properly. A sample of 8 components is sampled. Find probability that:

A) all work properly.

B) 6 work properly.

C) at most 3 work properly.

D) at least 1 works properly.

## Calculating the Probability of a Wheel Spun

A wheel with the following probabilities is spun:

Prob(1)= 0.50, Prob (2) = 0.20, Prob (3) = 0.30

If the wheel is spun 3 times find probability that the sum of numbers you get = 6

## Coin Toss and Die Roll Probability

A) A coin is tossed 20 times. Find probability of getting at least 14 heads.

B) A die is tossed 20 times. Find probability of getting a “1” two times.

C) Three dice are tossed. Find probability that a four shows on exactly two of the dice.