In a group of ten students each student has a probability of

In a group of ten students, each student has a probability of 0.7 of passing an exam. What is the probability that exactly 7 of them will pass?

Solution

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 =    10      
p = the probability of a success =    0.7      
x = the number of successes =    7      
          
Thus, the probability is          
          
P (    7   ) =    0.266827932 [ANSWER]