Respuesta :
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
[tex]X \sim B(n,p)[/tex]
The probability that out of n trials, there'd be x successes is given by
[tex]P(X =x) = \: ^nC_xp^x(1-p)^{n-x}[/tex]
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 × [tex]10^{-5}[/tex]
- P(getting exactly 10 correct) = 9.54 × [tex]10^{-7}[/tex]
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:
[tex]P(X \geq 7)[/tex]
This can be rewritten as:
[tex]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[/tex]
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:
https://brainly.com/question/13609688
