Question

Using the information on the left, combine the individual probabilities to compute the probability that Peter will pass the quiz. 0. 001 0. 002 0. 0035 0. 5.

Answer 1

The probability that Peter will pass the quiz is given by the option 3: 0.0035

How to find that a given condition can be modeled by binomial distribution?

Binomial distributions consists of n independent Bernoulli trials.

Bernoulli trials are those trials which end up randomly either on success (with probability p) or on failures( with probability 1- p = q (say))

Suppose we have random variable X pertaining binomial distribution with parameters n and p, then it is written as

$X \sim B(n,p)$

The probability that out of n trials, there'd be x successes is given by

$P(X =x) = \: ^nC_xp^x(1-p)^{n-x}$

For the considered case, the problem's statement is missing some facts.

They are:

Number of multiple choice questions in test = 10

Peter uses guessing for answering the questions.

To pass the test, Peter needs to get at least 7 correct answers.

Some probabilities on left are:

• P(getting exactly 7 correct) = 0.0031
• P(getting exactly 8 correct) = 0.000386
• P(getting exactly 9 correct) = 2.86 × $10^{-5}$
• P(getting exactly 10 correct) = 9.54 × $10^{-7}$

Let X be the number of questions peter gets correct in his test.

Then, the probability that he will pass the test is denoted as:

$P(X \geq 7)$

This can be rewritten as:

$P(X \geq 7) = P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)\\P(X \geq 7) =0.0031 + 0.000386 + 0.0000286 + 0.000000954 = 0.003515554$

This is approximately 0.0035

Thus, the probability that Peter will pass the quiz is given by the option 3: 0.0035

Learn more about binomial distribution here:

brainly.com/question/13609688