Mimi just started her tennis class three weeks ago On averag

Mimi just started her tennis class three weeks ago. On average, she is able to return 10% of her opponent’s serves. If her opponent serves 10 times, answer the following questions:

(a) Assume random number X is the number of serves Mimi returns. As we know, X follows a binomial distribution. What is n (the number of trials) , p (probability of success in each trial) and q (probability of failure in each trial)?

(b) What is the probability that she returns at least 2 of the 10 serves from her opponent? (Show work and round the answer to 4 decimal places)

(c) How many serves can she expect to return? (Hint : What is the expected value?) (Show work and round the answer to 2 decimal places)

Solution

A)
Here,

n=10
p=0.1
q=1-0.1=0.9 (answers)

B)

Note that P(at least 2) = 1 - P(at most 1).          
          
Using a cumulative binomial distribution table or technology, matching          
          
n = number of trials =    10      
p = the probability of a success =    0.1      
x = our critical value of successes =    2      
          
Then the cumulative probability of P(at most 1) from a table/technology is          
          
P(at most   1   ) =    0.736098929
          
Thus, the probability of at least   2   successes is  
          
P(at least   2   ) =    0.2639 (answer)

C)
Note that

Expected value=np=(10)(0.1)= 1.00 (answer)