A certain player makes a successful first serve 80% of the time. Assume that everything is independent. The propbability that she gets at least 4 serves in is_____? and that she gets no more than 3 serves in is_____?
Out of how many ?
Anyway Google binomial distribution
eg
http://stattrek.com/online-calculator/binomial.aspx
To calculate the probability that the player gets at least 4 serves in, we need to consider the complementary probability of getting no more than 3 serves in.
The probability of a successful first serve is 80%, which means the probability of an unsuccessful first serve (missing the serve) is 20%.
To get no more than 3 serves in, we need to calculate the probability of missing the serve on all 4 attempts. Since the events are independent, we can multiply the probabilities:
Probability of missing the first serve: 20% or 0.2
Probability of missing the second serve: 20% or 0.2
Probability of missing the third serve: 20% or 0.2
Probability of missing the fourth serve: 20% or 0.2
To find the probability of at least getting 4 serves in, we need to subtract the probability of getting no more than 3 serves in (missing all 4 attempts) from 1.
Probability of getting at least 4 serves in = 1 - Probability of getting no more than 3 serves in
Probability of getting at least 4 serves in = 1 - (0.2 * 0.2 * 0.2 * 0.2)
= 1 - 0.0016
= 0.9984
So, the probability that the player gets at least 4 serves in is 0.9984 or 99.84%.
To find the probability that she gets no more than 3 serves in, we have already calculated it as (0.2 * 0.2 * 0.2 * 0.2) = 0.0016.
So, the probability that the player gets no more than 3 serves in is 0.0016 or 0.16%.