A fair coin with 1 marked on one face and 6 on the other and a fair die are both tossed. Find the probability that the sum of numbers that turn up is (i) 3 (ii) 12

Solution:

Since the fair coin has 1 marked on one face and 6 on the other, and the die has six faces that are numbered 1, 2,3, 4, 5 and 6, the sample space is given by

S = {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6)

       (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}

Accordingly, n (S) = 12

(i) Let A be the event in which the sum of numbers that turn up is 3.

Accordingly, A = {(1, 2)}

Then the required probability is,

P (A) = Number of outcomes favourable to A/Total number of possible outcomes

= n (A)/n (S)

= 1/12

(ii) Let B be the event in which the sum of numbers that turn up is 12

Accordingly, B = {(6, 6)}

P (B) = Number of outcomes favourable to B/Total number of possible outcomes

= n (B)/n (S)

= 1/12

---

NCERT Solutions Class 11 Maths Chapter 16 Exercise 16.3 Question 5

A fair coin with 1 marked on one face and 6 on the other and a fair die are both tossed. Find the probability that the sum of numbers that turn up is (i) 3 (ii) 12.

Summary:

A fair coin with 1 marked on one face and 6 on the other and a fair die are both tossed.  Then the probabilities of the given events are (i) 1/12 (ii) 1/12