Three coins are tossed simultaneously. What is the probability of

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 = $\frac{favourable~outcomes}{Total~outcomes}$

∴ Probability of getting at least 1 head = $\frac{7}{8}$

Therefore, the probability of getting at least 1 head is $\frac{7}{8}$

(ii) Probability of exactly two tails:

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

∵ Probability = $\frac{favourable~outcomes}{Total~outcomes}$

∴ Probability of getting exactly 2 tails = $\frac{3}{8}$

Therefore, the probability of getting exactly two tails is $\frac{3}{8}$

(ii) Probability of at most one tail:

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

∵ Probability = $\frac{favourable~outcomes}{Total~outcomes}$

∴ Probability of getting at most 1 tail = $\frac{3}{8}$

Therefore, the probability of getting at most one tail is $\frac{3}{8}$

Please press Heart if you liked the solution.

Contact us