5. A bowl contains 7 chips, which cannot be distinguished by a sense of touch al

Question

5. A bowl contains 7 chips, which cannot be distinguished by a sense of touch alone. Three of the chips are marked $1 each, two are marked $3 each and the last 2 are marked $5 each. A player is blindfolded and draws, at random and without replacement, two chips from the bowl. The player is paid an amount equal to the sum of the values of the two chips that he draws and the game is over. a) What is the expected value of the game? b) What should be charged for the house to expect to make $2.00 6. An airline, believing that 5% of passengers fail to show up for flights, overbooks (sell more tickets than there are seats). Suppose a plane will hold 265 passengers, and the airline sells 275 seats. What's the probability that the airline will not have enough seats so someone gets bumped? Denver Colorado is prone to severe hailstorms. Insurance agents claim that a homeowner in Denver can expect to replace his or her roof (due to hail damage) once every 15 years. What is the probability that in 12 years, a homeowner in Denver will need to replace the roof twice because of hail. 7. 8. Medflight emergency helicopter service is available for medical emergencies occurring 15 to 110 miles from the hospital. A long-term study of the service shows that the response time from receipt of the dispatch call to arrival at the scene of the emergency is normally distributed with standard deviation of 11 minutes. What is the mean response time (to the nearest whole minute) if only 9.2% of the calls require more than 45 minutes to respond?

Explanation / Answer

Since there are 4 questions on the image and chegg policy tells us to answer only one question per request I am answering the 5th question, so please rate accordingly

5) a)

We have 3 chips of $1, 2 for $2 and 2 for $5

And two chips are drawn without replacement.

So the expected value of the game is the all the scenarios combined expected value

If X is the game then

For notation let

E[i,i] = Expected value of drawing $i coin on first draw and $j coin on 2nd draw

Then

E[1,1] = Expected value of drawing $1 coins on both draws = 3/7*1*2/6*1 = 6/42 = 1/7

Therefore

E(X) = E[1,1] + E[1,3] + E[1,5] + E[3,1] + E[3,3] + E[3,5] + E[5,1] + E[5,3] + E[5,5]

E(X) = 1/7 + 3/7*2/6*3 + 3/7*2/6*5 + 2/7*3/6*3 + 2/7*1/6*9 + 2/7*2/6*15+ 2/7*3/6*5 + 2/7*2/6*15 + 2/7*1/6*25

E(X) = 1/7 + 3/7 + 5/7 + 3/7 + 3/7 + 10/7+ 5/7 + 10/7 + 25/21

E(X) = (3 + 9 + 15+ 9+ 9 + 30 + 15 + 30 + 25)/21 = $6.90

b) If the house charges $6.9 then the house makes $0 on average

Thus for the house to make $2 , they should charge $8.9 for the game

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