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:

Exactly one mishap?

No mishaps?

Consider the experiment of rolling a single die. We are interested in observing an odd number. Indicate how we can introduce the concept of a random variable and state all the possible values it can assume.

Solution

a)

Here,

P(mishap) = 1 - 0.95 = 0.05.

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]

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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 =    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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