Probability

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niketdoshi123: Master | Next Rank: 500 Posts; Posts: 210; Joined: Thu Mar 08, 2012 11:24 pmFollowed by: 3 members; Thanked: 62 times

by niketdoshi123 » Fri Apr 20, 2012 10:58 pm

The probability is 1/2 that a certain coin will turn up heads on any given toss. If the coin is to be tossed three times, what is the probability that on at least one of the tosses the coin will turn up tails??

a)1/8
b)1/2
c)3/4
d)7/8
e)15/16

1-(1/2)^3= ans
Different Approach please!!

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Source: Beat The GMAT — Problem Solving | Fri Apr 20, 2012 10:58 pm

pemdas: Legendary Member; Posts: 1084; Joined: Fri Apr 15, 2011 2:33 pmFollowed by: 21 members; Thanked: 158 times

by pemdas » Sat Apr 21, 2012 2:16 am

your approach is the best as you found complement to P(at least 1 toss tail)=1-P(no toss tail)

here's another way, given we are dealing with a fair coin, i.e. p=0.5 (odds are equal) --> counting possible toss combination sets (3C1+3C2+3C3)(1/2)^3=7/8

niketdoshi123 wrote:The probability is 1/2 that a certain coin will turn up heads on any given toss. If the coin is to be tossed three times, what is the probability that on at least one of the tosses the coin will turn up tails??

a)1/8
b)1/2
c)3/4
d)7/8
e)15/16

1-(1/2)^3= ans
Different Approach please!!

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Sat Apr 21, 2012 2:30 am

niketdoshi123 wrote:The probability is 1/2 that a certain coin will turn up heads on any given toss. If the coin is to be tossed three times, what is the probability that on at least one of the tosses the coin will turn up tails??

a)1/8
b)1/2
c)3/4
d)7/8
e)15/16

1-(1/2)^3= ans
Different Approach please!!

Here's a slight variation.

Total possible outcomes:
Number of options for the first toss = 2. (Heads or tails.)
Number of options for the second toss = 2. (Heads or tails.)
Number of options for the third toss = 2. (Heads or tails.)
To combine these options, we multiply:
2*2*2 = 8.

Good outcomes:
Of the 8 possible outcomes, only one outcome is BAD: HHH.
This is the only way NOT to get at least one tails.
Thus, the number of GOOD outcomes = 8-1 = 7.

Good/Total = 7/8.

The correct answer is D.

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