Question

Max tossed a fair coin 3 times. What is the probability of getting heads in the first two trials and tails in the last trial?

 

 

Answer 1

`P\left( E \right) =\frac { 1 }{ 2 } * \frac { 1 }{ 2 } * \frac { 1 }{ 2 } =\frac { 1 }{ 8 }`

You could get this answer by creating a tree diagram or by thinking about the possibilities that exist.

Realm of possibilities with one toss:

H or T.

Realm of possibilities with two tosses:

H, H
H, T
T, H
T, T

Realm of possibilities with three tosses:

H, H, H
H, H, T <--- 1/8 chance of taking place
H, T, T
T, T, T
T, T, H
T, H, H
T, H, T
H, T, H

Answer 2

When you toss a coin 3 times here is what can happen:
H=heads
T= Tails
HHH TTT
HHT TTH
HTH THT
HTT THH
Since 8 things can happen and only one of them is what you want, the probability is 1/8
Another way to think about it is each toss has 1/2 of coming up as you want it to.
Three tosses are 1/2 x 1/2 x 1/2 which is 1/8