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# A fair coin is tossed 6 times. What is the probability that exactly 2

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Director
Joined: 07 Jun 2004
Posts: 555
Location: PA
A fair coin is tossed 6 times. What is the probability that exactly 2  [#permalink]

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Updated on: 15 Mar 2019, 03:45
3
2
00:00

Difficulty:

15% (low)

Question Stats:

76% (01:21) correct 24% (01:43) wrong based on 91 sessions

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A fair coin is tossed 6 times. What is the probability that exactly 2 heads will show.

A. 1/64
B. 7/64
C. 9/64
D. 15/64
E. 49/64

Originally posted by rxs0005 on 16 Jan 2005, 18:39.
Last edited by Bunuel on 15 Mar 2019, 03:45, edited 1 time in total.
Updated.
VP
Joined: 18 Nov 2004
Posts: 1154
Re: A fair coin is tossed 6 times. What is the probability that exactly 2  [#permalink]

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16 Jan 2005, 21:06
6C2(1/2)^6 = 15/64
Senior Manager
Joined: 21 Sep 2004
Posts: 453
Re: A fair coin is tossed 6 times. What is the probability that exactly 2  [#permalink]

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16 Jan 2005, 21:31
used binomial theorem for this one..
nCr* (p)^r (q)^n-r
probability of getting a head is 1/2=p
probability of NOT getting a head is 1/2=q
n=6
r=2

6C2 * (1/2)^2 * (1/2)^6-2
= 6C2*(1/2)^6
=15/64
Intern
Joined: 12 Aug 2004
Posts: 29
Re: A fair coin is tossed 6 times. What is the probability that exactly 2  [#permalink]

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18 Jan 2005, 14:05
I'm completely lost on this one, i've been studying for about 4 months and took some time off, now i'm paying for this "vacation", can someone show me the math used to get this answer?

Thanks
Intern
Joined: 20 Dec 2004
Posts: 25
Re: A fair coin is tossed 6 times. What is the probability that exactly 2  [#permalink]

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18 Jan 2005, 15:35
3
jeremy02 wrote:
I'm completely lost on this one, i've been studying for about 4 months and took some time off, now i'm paying for this "vacation", can someone show me the math used to get this answer?

Thanks

The probability of a particular event occurring is the number of outcomes that result in that particular event divided by the total number of possible outcomes.

-In this problem the total number of possible outcomes:
Since there are 2 possible outcomes for each coin toss, (2*2*2*2*2*2) = 64 which is the total number of possible outcomes.

-Now you can use the combination formula to determine the number of outcomes of exactly 2 of the coins landing on heads out of 6 flips.

C(n,r) =n!/(r!(n-r)!) where n = the number of n objects (n=6 flips) taken r (r=2; 2 out of 6 flips landing on heads) at a time.

6!/(2!(6-2)!) = 6!(2!(4!)= 15.

Once again, the probability of a particular event occurring is the number of outcomes that result in that particular event divided by the total number of possible outcomes.

# of outcomes that result in 2 flips out of 6 landing on heads = 15
total # of possible outcomes = 64

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Re: A fair coin is tossed 6 times. What is the probability that exactly 2  [#permalink]

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01 Nov 2018, 05:10
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Re: A fair coin is tossed 6 times. What is the probability that exactly 2   [#permalink] 01 Nov 2018, 05:10
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