A fair coin is tossed repeatedly. If tail appears on first four tosses, then the probability of head appearing on fifth toss equals

Question

A fair coin is tossed repeatedly. If tail appears on first four tosses, then the probability of head appearing on fifth toss equals (A) (1/2) (B) (1/32) (C) (31/32) (D) (1/5)

Tardigrade Admin · Accepted Answer

The event that the fifth toss results in a head is independent of the event that the first four tosses result in tails. ∴ Probability of the required event = 1/2

Q. A fair coin is tossed repeatedly. If tail appears on first four tosses, then the probability of head appearing on fifth toss equals

$\frac{1}{2}$

$\frac{1}{32}$

$\frac{31}{32}$

$\frac{1}{5}$

The event that the fifth toss results in a head is independent of the event that the first four tosses result in tails.
$∴$ Probability of the required event $= 1/2$

Q. A fair coin is tossed repeatedly. If tail appears on first four tosses, then the probability of head appearing on fifth toss equals

21​

321​

3231​

51​

The event that the fifth toss results in a head is independent of the event that the first four tosses result in tails. ∴ Probability of the required event =1/2

$\frac{1}{2}$

$\frac{1}{32}$

$\frac{31}{32}$

$\frac{1}{5}$

The event that the fifth toss results in a head is independent of the event that the first four tosses result in tails.
$∴$ Probability of the required event $= 1/2$