If a fair coin is tossed 3 times, what is the probability that it will turn up heads exactly twice?
answer : [spoiler] 3/8[/spoiler]
Is there any way of doing this without having to list out the possibilities like
HHH HHT HTT THT etc.
Probability
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imagine it like this Yes Yes No (YYN)
then we would have 1/2 * 1/2 * 1/2 = 1/8
but we are not done yet cause we have to multiply it with the number of possibilities the 2 Y can be arranged among the 3 spots of YYN.
therefore we have 1/8 * 3P3/2! = 1/8 * 3!/2! = 3/8
then we would have 1/2 * 1/2 * 1/2 = 1/8
but we are not done yet cause we have to multiply it with the number of possibilities the 2 Y can be arranged among the 3 spots of YYN.
therefore we have 1/8 * 3P3/2! = 1/8 * 3!/2! = 3/8
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I think that listing is a great way to solve this question. Too many students discount this approach.Aishwarya1204 wrote:If a fair coin is tossed 3 times, what is the probability that it will turn up heads exactly twice?
answer : [spoiler] 3/8[/spoiler]
Is there any way of doing this without having to list out the possibilities like
HHH HHT HTT THT etc.
Here's a more mathematical approach:
P(exactly 2 heads) = P(THH OR HTH OR HHT)
= P(THH) + P(HTH) + P(HHT)
= (1/2)(1/2)(1/2) + (1/2)(1/2)(1/2) + (1/2)(1/2)(1/2)
= (1/8) + (1/8) + (1/8)
= [spoiler]3/8[/spoiler]
Cheers,
Brent