The probability to pass financial accounting is 0.20,

ingabire aline

ingabire aline

Answered question

2022-08-06

The probability to pass financial accounting is 0.20, seven selected at random. Find the probability that 

a) fewer than 3 are able to pass

b) exactly 3 are able to pass

C) more than 3 are able to pass

D) at least 3are able to pass

Answer & Explanation

Don Sumner

Don Sumner

Skilled2023-05-23Added 184 answers

To solve the given problem, let's calculate the probabilities using the binomial probability formula. The binomial probability formula is given by:
P(X=k)=(nk)pk(1p)nk
where:
- P(X=k) is the probability of exactly k successes,
- n is the total number of trials,
- p is the probability of success in a single trial,
- k is the number of successes.
Given information:
- The probability to pass financial accounting is 0.20.
- We are selecting seven students at random.
a) Probability that fewer than 3 are able to pass:
To calculate this probability, we need to find the sum of the probabilities of having 0, 1, and 2 successful students.
P(fewer than 3)=P(X=0)+P(X=1)+P(X=2)
Using the binomial probability formula:
P(fewer than 3)=(70)·0.200·(10.20)7+(71)·0.201·(10.20)6+(72)·0.202·(10.20)5
b) Probability that exactly 3 are able to pass:
To calculate this probability, we need to find the probability of having 3 successful students.
P(exactly 3)=P(X=3)
Using the binomial probability formula:
P(exactly 3)=(73)·0.203·(10.20)73
c) Probability that more than 3 are able to pass:
To calculate this probability, we need to find the sum of the probabilities of having 4, 5, 6, and 7 successful students.
P(more than 3)=P(X=4)+P(X=5)+P(X=6)+P(X=7)
Using the binomial probability formula:
P(more than 3)=(74)·0.204·(10.20)74+(75)·0.205·(10.20)75+(76)·0.206·(10.20)76+(77)·0.207·(10.20)77
d) Probability that at least 3 are able to pass:
To calculate this probability, we need to find the sum of the probabilities of having 3, 4, 5, 6, and 7 successful students.
P(at least 3)=P(X=3)+P(X=4)+P(X=5)+P(X=6)+P(X=7)
Using the binomial probability formula:
P(at least 3)=(73)·0.203·(10.20)73+(74)·0.204·(10.20)74+(75)·0.205·(10.20)75+(76)·0.206·(10.20)76+(77)·0.207·(10.20)77
Now, you can substitute the values into the formulas and calculate the probabilities accordingly.

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