Assume that random guesses are made for eight multiple choice questions on an SA

Kyran Hudson

Kyran Hudson

Answered question

2021-10-01

Assume that random guesses are made for eight multiple choice questions on an SAT test, so that there are n=8 trials, each with probability of success (correct) given by p=0.20. Find the indicated probability for the number of correct answers.
Find the probability that the number x of correct answers is fewer than 3.

Answer & Explanation

toroztatG

toroztatG

Skilled2021-10-02Added 98 answers

Step 1
Binomial Probability:
The formula for binomial probability is as follows:
P(x)=nCx(p)x(1p)nx
Step 2
Probability that the number of x of correct answers is fewer than 3:
Here x follows binomial distribution.
Here, n is 8; p is 0.20.
The probability that the number of x of correct answers is fewer than 3 is obtained as 0.797, as shown below:
P(fewer than 3)=P(0)+P(1)+P(2)
=[{8}C0(0.2)0(10.2)80]+[{8}C1(0.2)1(10.2)81]+[{8}C2(0.2)0(10.2)82]
=0.168+0.335+0.294
=0.797

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