probability problem

Question

If you toss a coin 3 times what is the probability you will get 2 heads

Answer 1

Jon is correct. This is an ambiguous question . The question is PROBABLY ASKING for

exactly 2 heads like Jon says but

you could ask your prof if he/she means AT LEAST. I can argue that if I got three heads well... that means I got 2 .

1st coin heads or tails. ( 2 outcomes)

2nd coin heads or tails ( 2 outcomes)

3rd coin heads or tails ( 2 outcomes)

so 2x2x2= 8 outcomes listed below

HHH

HHT

HTH

HTT

THH

THT

TTH

TTT

4 of these equally likely outcomes are exactly 2 heads

so P( exactly 2 heads) = 4/8 = 1/2 ** probably**

5 of these have AT LEAST two heads so P( at least 2 heads) = 5/8

Answer 2

Use binomial formula:

x = number of tries

k = number of successes (in this case getting a head)

p = probability of getting a head

P(x,k) = C(x,k) p^k * (1-p)^(n-k), where C(x,k) = x!/(k!(n-k!))

For this problem, x = 3, k = 2 and p = 1/2