Compute the following binomial probabilities directly from t

Compute the following binomial probabilities directly from the formula for b(x;n,p).

b(3; 8, .7)

b(5; 8, .7)

P(3 X 5) when n = 8 and p = .7

P(X 1) when n = 10 and p = .1

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 =    8      
p = the probability of a success =    0.7      
x = the number of successes =    3      
          
Thus, the probability is          
          
P (3; 8; 0.7) =    0.04667544 [ANSWER]

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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 =    0.7      
x = the number of successes =    5      
          
Thus, the probability is          
          
P (5; 8; 0.7) =    0.25412184 [ANSWER]

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