Samantha leaves her house and drives 18 kilometers east to her friend's house. She then drives north to school. Finally, she dri
ves 30 kilometers directly home, in a straight line, from school. A map of Samantha's route is provided below.
How far does Samantha drive traveling from her friend's house to the school?
A.
42 kilometers
B.
12 kilometers
C.
35 kilometers
D.
24 kilometers
How far does Samantha drive traveling from her friend's house to the school?
A.
42 kilometers
B.
12 kilometers
C.
35 kilometers
D.
24 kilometers
2 answers:
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Answer:
a) 0.0797 = 7.97% probability that the next home run will be on his fifth at-bat.
b) The expected number of at-bats until the next home run is 6.25.
Step-by-step explanation:
For each at bat, there are two possible outcomes. Either it is a home run, or it is not. The probability of an at bat resulting in a home run is independent of any other at-bat, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
In which is the number of different combinations of x objects from a set of n elements, given by the following formula.
And p is the probability of X happening.
The probability that Barry Bonds hits a home run on any given at-bat is 0.16
This means that
Part A: What is the probability that the next home run will be on his fifth at-bat?
0 on his next 4(P(X = 0) when n = 4)
Home run on his 5th at-bat, with 0.16 probability. So
0.49787136 *0.16 = 0.0797.
0.0797 = 7.97% probability that the next home run will be on his fifth at-bat.
Part B: What is the expected number of at-bats until the next home run?
The expected number of trials for n successes is given by:
In this question, . So
The expected number of at-bats until the next home run is 6.25.