An experiment consists of tossing a fair coin 3 times What i

An experiment consists of tossing a fair coin 3 times.

What is the probability that you are going to have exactly 2 heads?

What is the probability that you are going to have at most 2 tails?

Please show work.

Solution

a)

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 =    3      
p = the probability of a success =    0.5      
x = the number of successes =    2      
          
Thus, the probability is          
          
P (    2   ) =    0.375 [ANSWER]

*****************

B)

Using a cumulative binomial distribution table or technology, matching          
          
n = number of trials =    3      
p = the probability of a success =    0.5      
x = the maximum number of successes =    2      
          
Then the cumulative probability is          
          
P(at most   2   ) =    0.875 [answer]