1. A fair coin is flipped 9 times. What is the probability of getting exactly 6

Question

1. A fair coin is flipped 9 times. What is the probability of getting exactly 6 heads?

2. Suppose that 10,000 U.S. licensed drivers are randomly selected. a. How many would you expect to be male? b. Using the table or tree diagram, construct a contingency table of gender versus age group. c. Using the contingency table, find the probability that out of the age 20–64 group, a randomly selected driver is female.

3. You buy a lottery ticket to a lottery that costs $10 per ticket. There are only 100 tickets available to be sold in this lottery. In this lottery there are one $500 prize, two $100 prizes, and four $25 prizes. Find your expected gain or loss.

Explanation / Answer

1.

Note that the probability of x successes out of n trials is          
          
P(n, x) = nCx p^x (1 - p)^(n - x)          
          
where          
          
n = number of trials =    9      
p = the probability of a success =    0.5      
x = the number of successes =    6      
          
Thus, the probability is          
          
P (    6   ) =    0.1640625 [ANSWER]

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