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## Homework Statement

A coin is tossed three times. I am asked for the probability that EITHER the first toss yields heads, OR the second toss yields tails, OR the third yields heads. I am expected to use De Morgan's Laws but am not sure how to define the events the themselves. I'd appreciate some guidance.

## Homework Equations

## The Attempt at a Solution

I have found the reuested probability using the following table

First toss: HTT

Second toss: HTH

Third toss: TTH

to be 3/8.

But how may I show that rigorously? Mind you, we haven't dealt with multiplication of probabilities (so (1/2)

^{3}for each case, let's say, would not be legit). We have hitherto only dealt with De Morgan's Laws, P(AUB)=P(A)+P(B)-P(A and B), and P(AUBUC)=P(A)+P(B)+P(C)-P(A and B) - P(B and C) - P(A and C) + P(A and B and C).

As mentioned, I'd appreciate your assistance.