Question

We are given three coins: one has heads in both faces, the second has tails in both faces, and the third has a head in one face and a tail in the other. We choose a coin at random, toss it, and it comes heads. What is the probability that the opposite face is tails?(a) 1/4(b) 1/3(c) 2/3(d) 1/2(e) 2/5

Answer 1

Pr(opposite face is tail) = 1/4. = Option (a)

Explanation:

From the illustration,

=> 1st coin has head both side

=> 2nd coin has tail both side

=> 3rd coin has head and tail.

If we toss a coin at random and head comes up; it implies that it can never have been the 2nd coin.

Consequently, we are left with only two coins (the 1st and the 3rd coin). Now, total number of coin that remain in the sample = 2.

Meanwhile,

=> the probability of tail from the 1st coin is ZERO

=> the probability of tail from the 3rd coin is 1/2.

Therefore, the probability of opposite face is tail is:

Pr(opposite face is tail) = (0+ 1/2)/2 = 1/4