Q) Three coins are tossed simultaneously. What is the probability of getting
(i) at least one head?
(ii) exactly two tails?
(iii) at most one tail?

Ans:

Since a coin has two possible outcomes (H, T)

∴ Total outcomes of 3 coins = 23 = 8

[i.e. (H, H, T), (H, H, H), (H, T, T), (H, T, H), (T, H, T), (T, H, H), (T, T, T), (T, T, H)]

(i) Probability of at least one head:

Possible outcomes of at least one head = Total outcomes – outcomes with ZERO head

∵ outcomes with ZERO head = 1    (T,T,T)

∴ outcomes of at least one head = 8 – 1 = 7

∵ Probability =

∴ Probability of getting at least 1 head =

Therefore, the probability of getting at least 1 head is

(ii) Probability of exactly two tails:

∵ Outcomes with exactly two tails = 3                   [(H,T,T), (T,H,T), (T,T,H)]

∵ Probability =

∴ Probability of getting exactly 2 tails =

Therefore, the probability of getting exactly two tails is

(ii) Probability of at most one tail:

∵ outcomes with at most one tail = 3        [(T, H, H), (H, T, H), (H, H, T)]

∵ Probability =

∴ Probability of getting at most 1 tail =

Therefore, the probability of getting at most one tail is

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