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  • A die is loaded in such a way that each odd number is twice as likely to occur as each even number. Find P(G), where G is the event that a number greater than 3 occurs on a single roll of the die.

A die is loaded in such a way that each odd number is twice as likely to occur as each even number. Find P(G), where G is the event that a number greater than 3 occurs on a single roll of the die.

Answers (1)

Probability of odd nos. = 2 x (probability of even no.)      ……….. (given)

Thus, P (Odd) = 2 x P (Even)

P(Odd) + P(Even) = 1

2P (Even) + P (Even) = 1

3P (Even) = 1

Thus, P (Even) = 1 / 3

Thus, P (Odd) = 1 – 1/3

                        = 3 – 1/ 3

                        = 2 / 3

Total no. occurring on a single roll = 6

& 4, 5 & 6 are the nos. greater than 3

Let P(no. greater than 3) = P (G)

                                    = P (no. is 4, 5 or 6)

Here, 4 & 6 – Even & 5 – Odd

Thus, P (G) = 2 x P (Even) x P (Odd)

                        = 2 x 1/3 x 2/3

                        = 4/9                   

Therefore, 4/9 is the required probability.

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