What is the probability that at most two students are smoker

What is the probability that at most two students are smoker What is the probability that none of them are smoker

Solution

a)

Using a cumulative binomial distribution table or technology, matching          
          
n = number of trials =    8      
p = the probability of a success =    0.2      
x = the maximum number of successes =    2      
          
Then the cumulative probability is          
          
P(at most   2   ) =    0.79691776 [ANSWER]

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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 =    8      
p = the probability of a success =    0.2      
x = the number of successes =    0      
          
Thus, the probability is          
          
P (    0   ) =    0.16777216 [ANSWER]