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Coin Probab

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by zagcollins » Sun Jul 20, 2008 5:26 am
When tossed, a certain coin has equal probability of landing on either side. If the coin is tossed 3 times, what is the probability that it will land on the same side each time?

A. 1/8
B. 1/4
C. 1/3
D. 3/8
E. 1/2

my answer is B...wrote down the probable outcomes..i.e.

HHH
TTT
HTT
HHT
THH
TTH
THT
HTH

Now we need heads on all three tries or tails on all three tries...so using the formula for discrete probab: desired outcome/total possible outcome

2/8= 1/4

I think my solution and approach, both, are correct...Pls advise if there's a simpler way to tackle this problem...
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by Saule » Sun Jul 20, 2008 7:42 am
I think it's actually 1/8 since 1/2*1/2*1/2=1/8.
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by Saule » Sun Jul 20, 2008 8:08 am
sorry, i forgot to multiply by 2.
so it's 1/8*2, since both sides count.
and equals to 1/4, which was your original answer :)
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by varnit » Sun Jul 20, 2008 10:42 pm
How I see it :

Either all three head or all three tail

(1/2)^3 + (1/2)^3
= 2/8 = 1/4
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by zagcollins » Mon Jul 21, 2008 4:24 am
not bad, varnit...thats a shortcut...thats what we need in math..faster ways to blow the problems out of the water!
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by Scott@TargetTestPrep » Wed Dec 13, 2017 1:11 pm
zagcollins wrote:When tossed, a certain coin has equal probability of landing on either side. If the coin is tossed 3 times, what is the probability that it will land on the same side each time?

A. 1/8
B. 1/4
C. 1/3
D. 3/8
E. 1/2
We need to determine the probability that a coin lands on the same side for all 3 tosses of the coin. This means that the 3-toss outcome will be either H-H-H or T-T-T.

P(T-T-T) = 1/2 x 1/2 x 1/2 = 1/8

P(H-H-H) = 1/2 x 1/2 x 1/2 = 1/8

Thus, the probability that the coin lands on the same side each time is 1/8 + 1/8 = 2/8 = 1/4.

Answer: B

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by Brent@GMATPrepNow » Wed Dec 13, 2017 1:31 pm
zagcollins wrote:When tossed, a certain coin has equal probability of landing on either side. If the coin is tossed 3 times, what is the probability that it will land on the same side each time?

A. 1/8
B. 1/4
C. 1/3
D. 3/8
E. 1/2
P(3 matching tosses) = P(ANY result on 1st toss AND 2nd toss matches 1st toss AND 3rd toss matches 2nd toss)
= P(ANY result on 1st toss) x P(2nd toss matches 1st toss ) x P(3rd toss matches 2nd toss)
= 1 x 1/2 x 1/2
= 1/4
= B

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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