Question

A baseball player has a batting average of 0.26. What is the probability that he has exactly 2 hits in his next 7 at bats

Answer 1

Answer:

The probability is  $P(2) = 0.426$

Step-by-step explanation:

From the question we are told that

         The probability of  success is $p = 0.26$

          The number of hits is  n =  7

         

Generally this probability follows a binomial distribution given there can only be two outcome i.e the probability of success and the probability of failure

       The probability of failure is  $q = 1- p$

substituting values

               $q = 1 - 0.26$

               $q = 0.74$

Now the probability of  exactly 2 hits in his next 7 at bats is mathematically evaluated as

     $P(2) = \left n} \atop {}} \right. C_2 *p^{2} * q^{n- 2}$

substituting values

    $P(2) = \left 7} \atop {}} \right. C_2 *p^{2} * q^{7- 2}$

Here $\left 7} \atop {}} \right. C_2$ means 7  combination 2 and using a calculator(reference calculator soup website) to compute, the value obtained is  

          $\left 7} \atop {}} \right. C_2 =21$

So

     $P(2) = 21 *(0.26)^{2} * (0.74)^{5}$

     $P(2) = 0.426$