Math probability

[Electrons]

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A coin is tossed and a die is rolled. Find the probability of a coin heads up or 4 on the die.

Answer: 1/2 + 1/6 - 1/12 = 7/12.

I can understand where the 1/2 and 1/6 come from, but why is it subtracting 1/12? I can't see the logic connection there.

 

[Streetwolf]

When you count each separately you are counting the case where they happen together, twice. The 1/2 is the odds of the coin coming out heads regardless of what the die says, so that includes the roll of 4. The 1/6 is the odds of the die coming out a 4, so that includes the flip of heads. Since this scenario (heads up, die 4) was counted twice with 1/2 + 1/6, you need to subtract the odds of both happening simultaneously ONCE to eliminate the twice counted value.

 

[Electrons]

Thanks. I get it now.

I guess the "and" could have been the hint to the linker.