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01 Feb 2021, 07:51
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
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Question Stats:
6% (01:47) correct
94%
(01:11)
wrong
based on 111
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What is the probability that all 6 coins tossed together will turn up heads, if it is known that 2 of them have turned up Heads?
A) 1/4
B) 1/16
C) 1/64
D) 1/57
E) 7/57
A) 1/4
B) 1/16
C) 1/64
D) 1/57
E) 7/57
26 May 2022, 14:52
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doomedcat
How about an easier way?!?!
How many total possible outcomes are there if we toss six coins? 2*2*2*2*2*2 = 2^6 = 64
But are all of those allowable? No, we need to eliminate any that don't have at least two heads.
How many ways are there to get 0 heads? 1
How many ways are there to get 1 heads? 6
Okay, so that's 7 configurations that aren't possible because we know we have to have at least two heads.
That leaves us with 64-7 = 57 allowable configurations.
How many of them "win?" Just one: HHHHHH.
So, the probability is 1/57.
Answer choice D.
For those who are curious, let's address why 1/2^4 doesn't work.
That would be the answer if we knew that two SPECIFIC coins landed heads. Imagine I say that first two coins land heads and ask what's probability that the remaining four also land heads. We'd have H H _ _ _ _. Now your 1/2^4 would work. But we just know that SOME two coins landed heads.
ThatDudeKnowsProbability
General Discussion
09 Feb 2021, 18:13
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doomedcat
Solution:
Since we know that 2 of the 6 coins will turn up heads, the probability that the other 4 coins will also turn up heads is ½ x ½ x ½ x ½ = 1/16.
Answer: B
