Q. 9

# On a multiple choice examination with three possible answers for each of the five questions, what is the probability that a candidate would get four or more correct answers just by guessing ?

Answer :

In this question, we have the repeated correct answer guessing form the given multiple choice questions are Bernouli trials

Let us now assume, X represents the number of correct answers by guessing in the multiple choice set

Now, probability of getting a correct answer,

Thus,

Clearly, we have X is a binomial distribution where n = 5 and

∴

Hence, probability of guessing more than 4 correct answer

= P (X = 4) + P (X = 5)

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A box has 100 pens of which 10 are defective. What is the probability that out of a sample of 5 pens drawn one by one with replacement at most one is defective?

Mathematics - ExemplarState True or False for the statements in the Exercise.

If A, B and C are three independent events such that P(A) = P(B) = P(C) = p, then

P (At least two of A, B, C occur) = 3p^{2} – 2p^{3}

A random variable X has the following probability distribution:

Determine:

(i) K (ii) P (X < 3)

(iii) P (X > 6) (iv) P (0 < X < 3)

**OR**

Find the probability of throwing at most 2 sixes in 6 throws of a single die

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Mathematics - Board Papers