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If six coins are flipped simultaneously, the probability of getting at
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22 Oct 2021, 06:54
22 Oct 2021, 06:54
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If six coins are flipped simultaneously, the probability of getting at least one heads and at least one tails is closest to
A) 3%
B) 6%
C) 75%
D) 94%
E) 97%
A) 3%
B) 6%
C) 75%
D) 94%
E) 97%
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: If six coins are flipped simultaneously, the probability of getting at
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22 Oct 2021, 07:16
22 Oct 2021, 07:16
1
Carcass wrote:
If six coins are flipped simultaneously, the probability of getting at least one heads and at least one tails is closest to
A) 3%
B) 6%
C) 75%
D) 94%
E) 97%
A) 3%
B) 6%
C) 75%
D) 94%
E) 97%
When it comes to probability questions involving "at least," it's 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 one heads and at least one tails) = 1 - P(not getting at least one heads and at least one tails)
What does it mean to not get at least one heads and at least one tails? It means getting EITHER zero heads OR zero tails.
So, we can write: P(getting at least one heads and at least one tails) = 1 - P(getting zero heads OR zero tails)
= 1 - P(getting ALL tails OR ALL heads)
P(getting ALL tails OR ALL heads)
= (tails on 1st toss AND tails on 2nd toss AND tails on 3rd toss AND tails on 4th toss AND tails on 5th toss AND tails on 6th toss OR heads on 1st toss AND heads on 2nd toss AND heads on 3rd toss AND heads on 4th toss AND heads on 5th toss AND heads on 6th toss)
= [1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2] + [1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2]
= [1/64] + [1/64]
= 2/64
= 1/32
So, P(getting at least one heads and at least one tails) = 1 - 1/32
= 31/32
≈ 97%
Answer: E
Cheers,
Brent
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GMAT 1: 700 Q51 V31
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WE:Engineering (Computer Software)
Re: If six coins are flipped simultaneously, the probability of getting at
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05 Oct 2022, 06:32
05 Oct 2022, 06:32
1
We need to find If six coins are flipped simultaneously, the probability of getting at least one heads and at least one tails is closest to
6 coins are tossed => Total number of cases = \(2^6\) = 64
Out of the these 64 cases we have TTTTTT, HHHHHH, and 62 cases where we have at least 1 Tail and at least 1 Head
=> P(At least 1T and At least 1H) = \(\frac{62}{64}\) = \(\frac{31}{32}\) ~ 97%
So, Answer will be E
Hope it helps!
Watch the following video to learn How to Solve Probability with Coin Toss Problems
6 coins are tossed => Total number of cases = \(2^6\) = 64
Out of the these 64 cases we have TTTTTT, HHHHHH, and 62 cases where we have at least 1 Tail and at least 1 Head
=> P(At least 1T and At least 1H) = \(\frac{62}{64}\) = \(\frac{31}{32}\) ~ 97%
So, Answer will be E
Hope it helps!
Watch the following video to learn How to Solve Probability with Coin Toss Problems
