1 Suppose you get a cash prize of 100 if you win a game The

1.) Suppose you get a cash prize of $100 if you win a game. The probability of winning the game is 0.6. What is the probability of winning between $600 and $800 inclusive if you play the game 10 times, assuming that each game is independent? Round to three decimals.

2.) Suppose you get a cash prize of $100 if you win a game. The probability of winning the game is 0.8. What is the probability of winning exactly $400 if you play the game 10 times, assuming that each game is independent? Round to three decimals.

3.) Suppose a community of 10 members want to build a bridge. Each member can either contribute $100 or nothing. The probability that a single member of the community contribute to the construction of the bridge is 0.65. Assuming that each member

Solution

Winning - cash prize 100 -- Prob =0.6

Let X be the no of winnings made.

X follows a Binomial distribution with p = 0.6 and n =10

the probability of winning between $600 and $800 inclusive if you play the game 10 times=

P(6<=x<=8)

= P(x<=8)-P(x<=5)

= 0.9536-0.3669

= 0.5867