Question

If we toss a fair coin and roll a fair die at the same time, then the probability of getting a 6 on the die and a head on the coin is:

A) 1/4

B) 2/3

C) 1/3

D) 1/12

Answer 1

The correct answer is D) 1/12 [ANSWER]

Explanation:

First we note that since, the die is fair, both the outcomes, head and tail, are equally likely. Thus,

P(heads) = (No. of favorable outcomes)/(Total no. of outcomes) = 1/2

Moreover, we are given that the die is fair, thus all the outcomes 1, 2, 3, 4, 5 and 6 are equally likely. Thus, we get:

P(6) = (No. of favorable outcomes)/(Total no. of outcomes) = 1/6

Now, clearly, the outcome of the coin does not have an impact on the outcome of the die and vice-versa. Thus, the coin and the die are independent.

Thus, the required probability is given by:

P(6 and heads) = P(6)*P(heads) [Since, the coin and die are independent]

= (1/6)*(1/2)

= 1/12 [ANSWER]

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