GATE CS 2016 Set 1 — Question 39
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Engineering Mathematics → Probability & Statistics → Sample Space & Events
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Question
Consider the following experiment.Step 1. Flip a fair coin twice.
Step 2. If the outcomes are (TAILS, HEADS) then output and stop.
Step 3. If the outcomes are either (HEADS, HEADS) or (HEADS, TAILS), then output and stop.
Step 4. If the outcomes are (TAILS, TAILS), then go to Step 1.The probability that the output of the experiment is is (up to two decimal places)
__________.
Step 2. If the outcomes are (TAILS, HEADS) then output and stop.
Step 3. If the outcomes are either (HEADS, HEADS) or (HEADS, TAILS), then output and stop.
Step 4. If the outcomes are (TAILS, TAILS), then go to Step 1.The probability that the output of the experiment is is (up to two decimal places)
__________.
Correct answer
0.33 to 0.34
Solution
Let
The sample space for two coin flips is , each with probability .
P(Y) be the probability that the output is .The sample space for two coin flips is , each with probability .
- Step 2: Outcome is . Probability is . Output is .
- Step 3: Outcomes are or . Probability is . Output is .
- Step 4: Outcome is . Probability is . The experiment repeats (goes back to Step 1).
P(Y) based on the first round of flips:Continue learning with Success Tracker
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