A basketball player can make 7 out of 10 free throws on aver

A basketball player can make 7 out of 10 free throws on average. Calculate the following probabilities that the basketball player will: a) makes 6 shots in a row? Hint: Find 6 success out of 6 b) misses 6 shots in a row? c) misses the first two shots and make the last two out of 4? Hint: Find 2 success out of 4 d) misses 5 shots out of 6?

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 =    6      
p = the probability of a success = 7/10 =   0.7      
x = the number of successes =    6      
          
Thus, the probability is          
          
P (    6   ) =    0.117649 [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 =    6      
p = the probability of a success =    0.7      
x = the number of successes =    0      
          
Thus, the probability is          
          
P (    0   ) =    0.000729 [ANSWER]

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C)

Here,

P(miss, miss, make, make) = 0.3*0.3*0.7*0.7 = 0.0441 [ANSWER]

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d)

This means making 1 attempt.

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 =    6      
p = the probability of a success =    0.7      
x = the number of successes =    1      
          
Thus, the probability is          
          
P (    1   ) =    0.010206 [ANSWER]