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Mathematics

Three unbiased coins are tossed together. What is the probability of getting at most two heads?

  1. (14)\Big(\dfrac{1}{4}\Big)

  2. (34)\Big(\dfrac{3}{4}\Big)

  3. (38)\Big(\dfrac{3}{8}\Big)

  4. (78)\Big(\dfrac{7}{8}\Big)

Probability

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Answer

When three coins are tossed together, the possible outcomes are: {(H, H, H), (H, H, T), (H, T, H), (T, H, H), (H, T, T), (T, H, T), (T, T, H), (T, T, T)}

Total number of outcomes = 8

Let E be the event of getting at most two heads,

E = {(H, H, T), (H, T, H), (T, H, H), (H, T, T), (T, H, T), (T, T, H), (T, T, T)}

The number of favorable outcomes to the event E = 7

∴ P(E) = Number of favorable outcomesTotal number of outcomes=78\dfrac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \dfrac{7}{8}

Hence, option 4 is the correct option.

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