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A coin is tossed and a die rolled. Find the probability of getting a head and an odd number. The answer is $\frac{1}{4}$.

My reasoning is that rolling an odd number is $\frac{1}{2}$, and tossing a coin on heads is $\frac{1}{2}$. So $0.5 \times 0.5$ = $\frac{1}{4}$.

Is this basically it?

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  • $\begingroup$ Yes. The outcome of the die is independent of the outcome of the coin: $P(d\cap c)=P(d|c)\cdot P(c)=P(d)\cdot P(c)$ $\endgroup$ – callculus Jul 7 '15 at 10:19
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Yes, this is it. The coin and the die are independent of each other, so you can just multiply the probabilities.

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