Question

Three coins are tossed together. Find the probability of getting:

(i) exactly two heads

(ii) at most two heads

(iii) at least one head and one tail

(iv) no tails

Answer 1

Given: Three coins are tossed simultaneously.

When three coins are tossed then the outcome will be anyone of these combinations.

TTT, THT, TTH, THH. HTT, HHT, HTH, HHH.

So, the total number of outcomes is 8.

(i) For exactly two heads, the favourable outcome are THH, HHT, HTH

So, the total number of favourable outcomes is 3.

We know that, Probability = Number of favourable outcomes/ Total number of outcomes

Thus, the probability of getting exactly two heads is 3/8

(ii) For getting at least two heads the favourable outcomes are HHT, HTH, HHH, and THH

So, the total number of favourable outcomes is 4.

We know that, Probability = Number of favourable outcomes/ Total number of outcomes

Thus, the probability of getting at least two heads when three coins are tossed simultaneously = 4/8 = 1/2

(iii) For getting at least one head and one tail the cases are THT, TTH, THH, HTT, HHT, and HTH.

So, the total number of favourable outcomes i.e. at least one tail and one head is 6

We know that, Probability = Number of favourable outcomes/ Total number of outcomes

Thus, the probability of getting at least one head and one tail = 6/8 = 3/4

(iv) For getting an outcome of no tail, the only possibility is HHH.

So, the total number of favourable outcomes is 1.

We know that, Probability = Number of favourable outcomes/ Total number of outcomes

Thus, the probability of getting no tails is 1/8.