Question

Let the probability of success on a Bernoulli trial be 0.28.

a. In five Bernoulli trials, what is the probability that there will be 4 failures? (Do not round intermediate calculations. Round your final answers to 4 decimal places.)

b. In five Bernoulli trials, what is the probability that there will be more than the expected number of failures? (Do not round intermediate calculations. Round your final answers to 4 decimal places.)

Answer 1

a)

Given that
n = number of trials =    5      
p = the probability of a success =    0.28      
x = the number of successes =    1      

The probability of x successes out of n trials is          
          
P(n, x) = nCx p^x (1 - p)^(n - x)  

The probability is P(1) = 0.3763   

b)

n = number of trials =    5      
p = the probability of a success =    0.28      
x = the maximum number of successes =    1      

The expected number of failures is

n(1-p) = 5*(1-0.28) = 3.6.

Then the cumulative probability is  P(at most 1) = 0.5697