aLets say we flip 10 times What is the probability that we g

a)Let\'s say we flip 10 times. What is the probability that we get 5 (and only 5) successes? In detail

b)Let\'s say we flip 10 times. What is the probability we get one or two successes? In detail

c)Let\'s say we flip 10 times. What is the probability we get 3 or less successes? In detail

Solution

a)

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 =    0.090909091      
x = the number of successes =    5      
          
Thus, the probability is          
          
P (    5   ) =    0.000971569 [ANSWER]

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b)

Note that P(between x1 and x2) = P(at most x2) - P(at most x1 - 1)          
          
Here,          
          
x1 =    1      
x2 =    2      
          
Using a cumulative binomial distribution table or technology, matching          
          
n = number of trials =    10      
p = the probability of a success =    0.090909091      
          
Then          
          
P(at most    0   ) =    0.385543289
P(at most    2   ) =    0.944581059
          
Thus,          
          
P(between x1 and x2) =    0.55903777   [ANSWER]

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c)

Using a cumulative binomial distribution table or technology, matching          
          
n = number of trials =    10      
p = the probability of a success =    0.090909091      
x = the maximum number of successes =    3      
          
Then the cumulative probability is          
          
P(at most   3   ) =    0.990846254 [ANSWER]