probability

[joey2007]

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Please help me how to do this problem without listing out the possible outcomes.

If a fair coin is flipped three times, what is the probability that the result will be tails exactly twice?

a) 1/8
b) 1/5
c) 3/8
d) 5/8
e) 2/3

thanks

 

[curiosteph]

Distinguishable permutations:

The probability of getting a heads then a tails then a tails is:

1/2 X 1/2 X 1/2 = 1/8

This is not the answer though . . . you have to factor in the number of different arrangements. To do this you take factorial of the number of coin flips (3) and divide it by the factorial number that have to match (2).

3!/2! = 3

Multiply 3 by 1/8 and you get (c) 3/8

Try it with four coins, and three of which have to be tails.

 

[joey2007]

hi... it is 1/4 for 4 coins w/ 3 tails???

Thanks!!!!!!!!!!!!!!!!

 

[curiosteph]

Yep!