Question

A fair coin is tossed five times. What is the probability of getting H,H,T,H,H in that order?

Answer 1

Answer:

Step-by-step explanation:

There are 32 possible outcomes when you toss a fair coin 5 times. You will always get one of the 32 outcomes. For example to could get 3 heads followed by 2 tails.

Each toss has only 2 outcomes: heads or tails. The way you get 32 is by

2 * 2 * 2 * 2 * 2 = 32.

You must get 1 of the 32 possible outcomes.

1 of them is the one you suggested

1/32 = 0.03125 is the probability that you want.

Answer 2

These questions can be confusing at times and the solution to such questions have not so common solutions. Before you read the answer let us unlearn everything we know and just apply some common logic of probability and permutations.
So how many heads do we want exactly = 3.
So let us see how many ways are there for selecting 3 places out of 5 places (the selection being unbiased).
We get numerator = 53
5
C
3
.
Now clearly what are the chances of anything head or tail for each selection is 1/2. So for 5 chances we get denominator = (1/2)5.
(
1
/
2
)
5
.
Our answer comes out to be
numerator/denominator = 5/16.
5
/
16.


Let us understand that this is the probability of getting exactly 3 tails out of the 5 chances too. Or any such other constraint which resonates with our logic of selection of 3 things out of 5 things (unbiased). So we just concentrated on how we can select 3 places with the provided constraint.