X is a binomial random variable with parameters n 16 and p

X is a binomial random variable with parameters n = 16 and p = 0.74. Compute the probability indicated. Please show work.

P(14)

P(4)

P(0)

P(20)

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 =    16      
p = the probability of a success =    0.74      
x = the number of successes =    14      
          
Thus, the probability is          
          
P (    14   ) =    0.11977661 [ANSWER]

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

b)

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 =    16      
p = the probability of a success =    0.74      
x = the number of successes =    4      
          
Thus, the probability is          
          
P (    4   ) =    0.0000520809 [ANSWER]

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

c)

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 =    16      
p = the probability of a success =    0.74      
x = the number of successes =    0      
          
Thus, the probability is          
          
P (    0   ) =    0.000000000436087 [ANSWER]

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

d)

We cannot have 20 successes as there are just 16 trials, Hence,

P(20) = 0 [ANSWER]