Conditional Coin Probability

P(B|A) with coin flip examples

P(First was Heads | Second is Heads)

Question

You flip two coins. Given that the second coin shows Heads, what is the probability that the first coin also showed Heads?

1st: ?

2nd: Heads

Let A = "second coin is Heads"

Let B = "first coin is Heads"

We want P(B|A)

2nd is H

2nd is T

2nd is H

2nd is T

Among outcomes where 2nd is H, how many have 1st as H?

Answer

This result confirms that coin flips are independent events!

They are the same! Knowing the second flip's result does not change the probability of the first flip. This is the definition of independence.