Question

Consider the following experiment:
Step - 1: Flip a fair coin twice.
Step - 2: If the outcomes are (TAILS, HEADS) the output is Y and stop.
Step - 3: If the outcomes are either (heads, heads) or (HEADS, TAILS), then output is N and stop.
Step - 4: If the outcomes are (TAILS, TAILS), then go to Step - 1.
The probability that the output of the experiment is Y is (upto two decimal places)

• A. 0.33

Answer 1

The correct option is A 0.33
Req. prob. $=P\left[TH\right]+P\left(TTTH\right)+P\left(TTTTTH\right)+.....$

$=\frac{1}{4}+\frac{1}{16}+\frac{1}{64}+.....$

$=\frac{1/4}{1-\frac{1}{4}}=\frac{1}{3}=0.33$