Tammy Fisher
2021-11-12
If a coin is flipped 100 times, the probability of obtaining 49 or fewer heads is 0.4602 and the probability of obtaining 50 heads is .0796
(a) what is the probability of obtaining more than 50 heads?
(b) what is the probability of obtaining at most 50 heads?
Robert Harris
Beginner2021-11-13Added 23 answers
Step 1
Given information:
It is given that a coin is flipped for 100 times. That is, . It is known that all the outputs of 100 flips will be independent of each other, imp-lying independence among each other. As a result, the 100 flips can be considered as 100 independent trials.
Consider the event that the outcome is head as a “success”. Consider the probability of getting head as p, that is, the probability of success in each trial is p. Then .
Consider X as the number of heads. Then, X has a Binomial distribution with parameters .
The pdf of X is given below:
Step 2 a) Obtain the probability of obtaining more than 50 heads.
It is given that the probability of obtaining at most 49 heads is
The probability of obtaining 50 heads is .
The probability of obtaining more than 50 heads is obtained as 0.4602 from the calculation given below:
Thus, the probability of obtaining more than 50 heads is 0.4602.
Step 3
b) Obtain the probability of obtaining at most 50 heads.
The probability of obtaining at most 50 heads is obtained as 0.5398 from the calculation given below:
Thus, the probability of obtaining at most 50 heads is 0.5398.
xleb123
Skilled2023-05-26Added 181 answers
Andre BalkonE
Skilled2023-05-26Added 110 answers
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