Question

a penny is tossed 5 times.

(a) Find the chance that the 5th toss is head.

(B) Find the chance that the 5th toss is head, given the first 4 are tails.

Answer 1

Solution :

Let us assume that the coin is fair, that is, the probabilities P( H ) = P( T ) = 0.5.

Where; H = getting Head and T = getting Tail

Suppose we toss the fair coin 5 times with each trial is independent, since getting an outcome ( H/T ) at first trial does not affect the probability of getting an outcome ( H/T ). Also P( H ) is same for each trial.

(a).

So the probabiity of getting head on 5th trial is; P( H ) = 0.5.

In other words; the chance that the 5th toss is head = 50%.

(b).

The chance that the 5th toss is head, given the first 4 are tails is given by;

P( H | TTTT ) = P( H ) ... { Since each trial is independent }

So P( H | TTTT ) = 0.5.

The chance that the 5th toss is head, given the first 4 are tails is 50%.