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liberstina [14]
3 years ago
10

A test has multiple choice questions with 5 choices for each answer; only one answer is correct for each question. Suppose a stu

dent guesses the answer to each question. Assuming the guesses are independent, find the probability that the student will not guess correctly on any one question.
a. 0
b. 1/5
c. 4/5
Mathematics
1 answer:
Ivenika [448]3 years ago
4 0
Number of choices per question = 5
Number of wrong answers = 4
P(wrong answer) = 4/5

Answer: 4/5
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Answer:

P(X = 0) = 0.027

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Step-by-step explanation:

The probability mass function P(X = x) is the probability that X happens x times.

When n trials happen, for each x \leq n, the probability mass function is given by:

P(X = x) = pe_{n,x}.p^{x}.(1-p)^{n-x}

In which p is the probability that the event happens.

pe_{n,x}, is the permutation of n elements with x repetitions(when there are multiple events happening(like one passes and two not passing)). It can be calculated by the following formula:

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The sum of all P(X=x) must be 1.

In this problem

We have 3 trials, so n = 3

The probability that a wafer pass a test is 0.7, so p = 0.7

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P(X = 2) = pe_{3,2}.(0.7)^{2}.(0.3) = 0.441

P(X = 3) = (0.7)^{3} = 0.343

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