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GATE | GATE-CS-2016 (Set 1) | Question 39

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Consider the following experiment.

Step 1. Flip a fair coin twice.
Step 2. If the outcomes are (TAILS, HEADS) then output Y and stop.
Step 3. If the outcomes are either (HEADS, HEAD) or (HEADS, TAILS), 
        then output 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 (up to two decimal places).

[This Question was originally a Fill-in-the-Blanks question]
(A) 0.33
(B) 0.25
(C) 0.5
(D) 0.27


Answer: (A)

Explanation:  

A fair coin is flipped twice => {(HH),(HT),(TH),(TT)} four outcomes.
Given, if (TH) comes, output ‘Y’.
If (HH),or (HT) comes, output ‘N’.
If (TT) comes, again flip coin twice.
Let, P = probability of getting (TH) or output ‘Y’=1/4.
Let, Q= probability of getting (TT) or again flipping coin twice =1/4.

Then, probability of getting output ‘Y’= probability of event ‘P’ occurring 1st time (OR) probability of event ‘P’ occurring 2nd time (OR) probability of event ‘P’ occurring 3rd time+……… =P+QP+QQP+QQQP+QQQQP…….
=(1/4)+(1/4*1/4)+ (1/4*1/4*1/4)+( 1/4*1/4*1/4*1/4)+……..

It is and infinite GP where, ‘a’=1/4 and ‘r’= 1/4.
So, answer= sum= (1/4)/(1-(1/4))=1/3=0.33

 

This solution is contributed by Sandeep pandey.

Quiz of this Question


Last Updated : 28 Jun, 2021
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