**Question:**

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

(a) exactly two heads

(b) at most two heads

(c) at least one head and one tail.

(d) no tails

**Solution:**

GIVEN: Three coins are tossed simultaneously.

TO FIND: We have to find the following probability

When three coins are tossed then the outcome will be

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

Hence total number of outcome is 8.

(i) For exactly two head we get favorable outcome as THH, HHT ,HTH

Hence total number of favorable outcome i.e. exactly two head 3

We know that PROBABILITY =

Hence probability of getting exactly two head is

(ii) In case, at least two head we have favorable outcome as TTT, THT, TTH, THH. HTT, HHT, HTH

Hence total number of favorable outcome i.e. at most two head is 7

We know that PROBABILITY =

Hence probability of getting at most two head when three coins are tossed simultaneously is equal to

(iiii) At least one head and one tail we get in case THT, TTH, THH. HTT, HHT, HTH,

Hence total number of favorable outcome i.e. at least one tail and one head is 6

We know that PROBABILITY =

Hence probability of getting at least one head and one tail is equal to

(iv) No tail i.e. HHH

Hence total number of favorable outcome is 1

We know that PROBABILITY =

Hence probability of getting no tail is