Question

A coin is tossed three times. If X denotes the absolute difference between the number of heads and the number of tails then P(X = 1) = ______.

Options

• `1/2`

• `2/3`

• `1/6`

• `3/4`

Answer 1

A coin is tossed three times. If X denotes the absolute difference between the number of heads and the number of tails then P(X = 1) = `underlinebb(3/4)`.

Explanation:

A coin is tossed 3 times.

∴ Possibilities are

HHH `rightarrow` X = 3 – 0 = 3

TTT `rightarrow` X = 3 – 0 = 3

HHT `rightarrow` X = 2 – 1 = 1

HTH `rightarrow` X = 2 – 1 = 1

THH `rightarrow` X = 2 – 1 = 1

HTT `rightarrow` X = 2 – 1 = 1

TTH `rightarrow` X = 2 – 1 = 1

THT `rightarrow` X = 2 – 1 = 1

∴ P(X = 1) = `6/8 = 3/4`