Amultiple-choice test consists of 20 questions with possible answers of a, b, c, d, e. estimate the probability that with random guessing, the number of correct answers is at least 9.

0.009982

Step-by-step explanation:

Given that a  multiple-choice test consists of 20 questions with possible answers of a, b, c, d, e.

If a person does not know any answer but simply guesses the probability for his correct guess is 0.20 since there are 5 choices.

Also each question guess is independent of the other and there are only two outcomes.

X the no of correct answered questions is binomial with p =0.20 and n = 20

the probability that with random guessing, the number of correct answers is at least 9

Given a Venn diagram containing three circles representing three sets, say A, B and C. The number representing the set A or B or C is given by the addition of all the elements inside the three circles excluding the element outside the three circles. Thus from the given Ven diagram n(P or B or C) = 10 + 2 + 8 + 4 + 6 + 5 + 7 = 42. The total number of elements in the Venn diagram (i.e. the universal set) = 42 + 8 = 50. P(A or B or C) = n(A or B or C) / n(Universal set) = 42 / 50 = 21 / 25