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Suppose you flip a fair coin six times. What is the probability that,
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06 Apr 2022, 08:29
06 Apr 2022, 08:29
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Suppose you flip a fair coin six times. What is the probability that, in six flips, you get at least one head?
(A) 5/8
(B) 13/16
(C) 15/16
(D) 31/32
(E) 63/64
(A) 5/8
(B) 13/16
(C) 15/16
(D) 31/32
(E) 63/64
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Re: Suppose you flip a fair coin six times. What is the probability that,
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06 Apr 2022, 08:33
06 Apr 2022, 08:33
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Carcass wrote:
Suppose you flip a fair coin six times. What is the probability that, in six flips, you get at least one head?
(A) 5/8
(B) 13/16
(C) 15/16
(D) 31/32
(E) 63/64
(A) 5/8
(B) 13/16
(C) 15/16
(D) 31/32
(E) 63/64
STRATEGY: When it comes to probability questions involving "at least," it's typically best to try using the complement.
That is, P(Event A happening) = 1 - P(Event A not happening)
So, here we get: P(getting at least 1 head) = 1 - P(not getting at least 1 head)
What does it mean to not get at least 1 head? It means getting ZERO heads.
So, we can write: P(getting at least 1 head) = 1 - P(getting zero heads)
P(getting zero heads)
P(getting zero heads) = P(1st flip is tails AND 2nd flip is tails AND 3rd flip is tails AND 4th flip is tails AND 5th flip is tails AND 6th flip is tails)
= P(1st flip is tails) x P(2nd flip is tails) x P(3rd flip is tails) x P(4th flip is tails) x P(5th flip is tails) x P(6th flip is tails)
= 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2
= 1/64
So, P(getting at least 1 head) = 1 - P(getting zero heads)
= 1 - 1/64
= 64/64 - 1/64
= 63/64
Answer: E
Re: Suppose you flip a fair coin six times. What is the probability that,
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06 Apr 2022, 08:58
06 Apr 2022, 08:58
total outcomes = 2^6 = 64
favourable outcome = atleast one head....the mutually exclusive event would be getting no head...i.e the outcome of TTTTTT..all tails so probability of getting all tail = 1/64
then atleast one head = 1-1/64 = 63/64
favourable outcome = atleast one head....the mutually exclusive event would be getting no head...i.e the outcome of TTTTTT..all tails so probability of getting all tail = 1/64
then atleast one head = 1-1/64 = 63/64
