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Question
Three coins are tossed once. Find the probability of getting
- 3 heads
- 2 heads
- at least 2 heads
- at most 2 heads
- no head
- 3 tails
- exactly two tails
- no tail
- atmost two tails.
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Solution
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`
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