Modern Math

Probability

Easy

When three coins are tossed simultaneously, what is the probability of getting exactly one tail?

5/8

3/8

7/8

1/8

✅ Correct Option: 2

Each coin has $2$ possible results: Head (H) or Tail (T).

Since there are $3$ coins, total number of outcomes $= 2^3 = 8$

All 8 outcomes: HHH, HHT, HTH, THH, HTT, THT, TTH, TTT

Outcomes with exactly one tail: HHT, HTH, THH

Favourable outcomes $= \binom{3}{1} = 3$

The single tail can appear on any one of the 3 coins, giving 3 arrangements.

$P(\text{exactly one tail}) = \dfrac{\text{Favourable Outcomes}}{\text{Total Outcomes}}$

$= \dfrac{3}{8}$

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