Mimi just started her tennis class three weeks ago. On average, she is able to r
ID: 3130930 • Letter: M
Question
Mimi just started her tennis class three weeks ago. On average, she is able to return 20% of her opponent’s serves. Assume her opponent serves 10 times.
(a) Let X be the number of returns that Mimi gets. As we know, the distribution of X is a binomial probability distribution. What is the number of trials (n), probability of successes (p) and probability of failures (q), respectively?
(b) Find the probability that that she returns at least 1 of the 10 serves from her opponent. Show all work. Just the answer, without supporting work, will receive no credit.
Explanation / Answer
A)
n = 10 (number of times an event is occuring / number of trials) beacause in this case opponent serves 10 times
Probability = Total number of favourable outcomes / Total number of outcomes
Therefore,
Probability of success
= Number of times Mimi is able to return the serves
Total number of serves made to Mimi
= ( 20 % of 10 ) i.e. 2
( 100 % of 10 ) i.e. 10
= 0.2
Similarly,
Probability of failure
= Number of times Mimi is not able to return the serves
Total number of serves made to Mimi
= ( 80 % of 10 ) i.e. 8
( 100 % of 10 ) i.e. 10
= 0.8
B)
The probability that Mimi returns at least 1 of the 10 serves from her opponent
= 1 - Probability that she doesn't return any serves
(Beacause favourable serves of atleast 1 return will be = { 1,2,3,4,5,6,7,8,9,10 } returns of 10 serves made.
Since, total probability of everything =1
Probability of 0 return + Probability of 1 return + Probability of 2 return + Probability of 3 return + Probability of 4 return + Probability of 5 return + Probability of 6 return + Probability of 7 return + Probability of 8 return + Probability of 9 return + Probability of all 10 return = 1
So,
1 - Probability of 0 serves return = Probability that Mimi returns atleast 1 serve )
P (x success ) = n C x ( Success probability ) x * ( Success of failure) ( n-x )
Therefore,
P (0 success) = 10 C 0 ( 0.2 ) 0 * ( 0.8 ) ( 10 - 0 )
= 10 C 0 ( 0.8 ) 10
= 10 ! ( 0.8 ) 10
0 ! ( 10 - 0 ) !
= 10 ! ( 0.8 ) 10
10 !
= ( 0.8 ) 10
Now,
Since
The probability that Mimi returns at least 1 of the 10 serves from her opponent
= 1 - Probability that she doesn't return any serves ( 0 serve return )
= 1 - ( 0.8 ) 10
This is the answer. All the best. :)