1)A student takes a 5 question multiple choice quiz with 4 choices for each ques

Question

1)A student takes a 5 question multiple choice quiz with 4 choices for each question. If the student guesses at random on each question, what is the probability that the student gets exactly 3 questions correct?

2)A student takes a true-false test that has 13 questions and guesses randomly at each answer. Let X be the number of questions answered correctly. Find P(11 or more)

4)Compute the probability of X successes.
n = 5, X = 4, p = 0.7

5)Determine whether the random variable described is discrete or continuous.
The total value of a set of coins

Explanation / Answer

1)

Solution :
Given that ,
p = 1 / 4 = 0.25
1 - p = 1 - 0.25 = 0.75
n = 5
Using binomial probability formula ,
P(X = x) = ((n! / x! (n - x)!) * px * (1 - p)n - x

P(X = 3) = ((5! / 3! (5 - 3)!) * 0.253 * (0.75)5 - 3

P(X = x) = ((5! / 3! (2)!) * 0.253 * (0.75)2 = 0.0879

The probability that the student gets exactly 3 questions correct is  0.0879 .

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