Assume that it is known that 95 percent of the launching of

Assume that it is known that 95 percent of the launching of satellites into orbit are successful. What is the probability that in the next four launching there will be

no mishaps?

exactly one mishap?

Solution

As 95% are successful, then 1 - 0.95 = 0.05 are mishaps.

a) NO MISHAPS:

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 =    4      
p = the probability of a success =    0.05      
x = the number of successes =    0      
          
Thus, the probability is          
          
P (    0   ) =    0.81450625 [ANSWER]

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b) ONE MISHAP:

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 =    4      
p = the probability of a success =    0.05      
x = the number of successes =    1      
          
Thus, the probability is          
          
P (    1   ) =    0.171475 [ANSWER]