Question

Three coins are tossed once. Find the probability of getting

1. 3 heads
2. 2 heads
3. at least 2 heads
4. at most 2 heads
5. no head
6. 3 tails
7. exactly two tails
8. no tail
9. atmost two tails.

Answer 1

If 3 coins are tossed, then the sample space of the experiment is

S = {HHH, HHT, HTH, THH, TTH, THT, HTT, TTT}

Total possible outcomes = 8

(i) Three heads {HHH} can appear in one way.

So the probability of getting 3 heads = `1/8`

(ii) There are three ways of getting 2 heads or 2 heads 1 tail, HHT, HTH, THH.

Total possible outcomes = 8

Probability of 2 heads appearing = `3/8`

(iii) To get a minimum of 2 heads, 2 heads 1 tail or 3 heads will occur

∴ A minimum of 2 heads can appear in four ways, HHT, HTH, THH, HHH.

Hence, the probability of minimum 2 heads appearing = `4/8`

= `1/2`

(iv) Maximum 2 heads will appear as follows.

(a) No head or three tails

(b) One head 2 tails

(c) 2 heads 1 tail

This {TIT, HTT, THT, TTH, HHT, HTH, THH} can appear in seven ways.

Total possible outcomes = 8

∴ Probability of maximum 2 heads appearing = `7/8`

(v) No head appearing means three tails appearing, which can happen in one way (TTT).

Total possible outcomes = 8

Hence, the probability of no head appearing = `1/8`

(vi) Three tails can appear in one way (TTT).

Probability of three tails appearing = `1/8`

(vii) Actually 2 tails (TTH, THT, HTT) can be obtained in three ways.

Total possible outcomes = 8

∴ Probability of two tails appearing = `3/8`

(viii) No tails means all three heads appear, so (HHH) can happen in only 1 way.

Total possible outcomes = 8

Probability of no tails appearing = `1/8`

(ix) Maximum two tails appearing

⇒ All three tails do not appear.

Probability of all three tails appearing = `1/8`

∴ Probability of maximum two tails appearing = 1 – (Probability of all three tails appearing)

= `1 - 1/8`

= `7/8`