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A coin tossed until a head appears or until the coin has been tossed 5 times. If a head does not occur on the first two tosses, then the probability that the coin will be tossed 5 times is
- a)1/6
- b)1/8
- c)1/12
- d)None of these
Correct answer is option 'D'. Can you explain this answer?
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A coin tossed until a head appears or until the coin has been tossed 5...
Solution:
Let P be the probability that the coin will be tossed 5 times.
Case 1: Head appears on the first or second toss.
In this case, the game ends and the probability of this happening is:
P(head on first toss) + P(head on second toss) = 1/2 + 1/4 = 3/4
Case 2: Head does not appear on the first two tosses.
In this case, the game continues and the probability of this happening is:
P(tail on first toss) x P(tail on second toss) = 1/2 x 1/2 = 1/4
Now, the probability that the coin will be tossed 5 times given that it did not appear on the first two tosses is:
P = P(tail on first toss) x P(tail on second toss) x P(tail on third toss) x P(tail on fourth toss) x P(head on fifth toss)
= 1/2 x 1/2 x 1/2 x 1/2 x 1/2 = 1/32
Therefore, the total probability of the coin being tossed 5 times is:
P = (3/4 x 0) + (1/4 x 1/32) = 1/128
Hence, the correct option is D) None of these.
Let P be the probability that the coin will be tossed 5 times.
Case 1: Head appears on the first or second toss.
In this case, the game ends and the probability of this happening is:
P(head on first toss) + P(head on second toss) = 1/2 + 1/4 = 3/4
Case 2: Head does not appear on the first two tosses.
In this case, the game continues and the probability of this happening is:
P(tail on first toss) x P(tail on second toss) = 1/2 x 1/2 = 1/4
Now, the probability that the coin will be tossed 5 times given that it did not appear on the first two tosses is:
P = P(tail on first toss) x P(tail on second toss) x P(tail on third toss) x P(tail on fourth toss) x P(head on fifth toss)
= 1/2 x 1/2 x 1/2 x 1/2 x 1/2 = 1/32
Therefore, the total probability of the coin being tossed 5 times is:
P = (3/4 x 0) + (1/4 x 1/32) = 1/128
Hence, the correct option is D) None of these.
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Community Answer
A coin tossed until a head appears or until the coin has been tossed 5...
None of these answer 'D' is correct
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A coin tossed until a head appears or until the coin has been tossed 5 times. If a head does not occur on the first two tosses, then the probability that the coin will be tossed 5 times isa)1/6b)1/8c)1/12d)None of theseCorrect answer is option 'D'. Can you explain this answer?
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