Question

# David and Carol play a game as follows: David throws a die, and Carol tosses a...

David and Carol play a game as follows: David throws a die, and Carol tosses a coin. If die falls "six", David wins. If the die does not fall "six" and the coin does fall heads, Carol wins. If neither the die falls "six" nor the coin falls heads, the foregoing is to be repeated as many times as necessary to determine a winner. Whant is the probability that David wins?

p(getting 6 on die) = 1/6

P(not getting 6 on die) = 1 - 1/6 = 5/6

Thus, P(david win) = P(win in 1st attempt) + P(win in 2nd attempt) and so on

Thus, P(david win) = 1/6 + 5/6*1/2*1/6 + 5/6*1/2*5/6*1/2*1/6 +  5/6*1/2*5/6*1/2*5/6*1/2*1/6 + ..

= 1/6 + 5/12*1/6 + (5/12)^2*1/6 + (5/12)^3*1/6 + ....

This is GP with a = 1/6, r = 5/12

Sum of GP = a/(1-r) when r < 1

Thus,

P(david win) = 1/6 / (1- (5/12))

= 1/6 * 12/7

= 2/7

#### Earn Coins

Coins can be redeemed for fabulous gifts.

##### Need Online Homework Help?

Most questions answered within 1 hours.

##### Active Questions
• Over the past several months, an adult patient has been treated for tetany (severe muscle spasms)....
• Suppose R>0. Which of the following statements might be true about a power series centered about...
• An Engineering consultant appointed on the construction of a Bridge site decided to conduct the Plate...
• Create a program in java using if statements Suppose the WIFI of a client is not...
• W Mart, one of major retailers, reported cash flows and earning: Comprehensive income) for the firm...
• Parker Hi-Fi Systems Parker Hi-Fi Systems, located in Wellesley, Massachusetts, a Boston suburb, assembles and sells...