<s>[INST] Weighted Coin Toss Probablity Suppose two weighted coins are tossed. The first is weighted so that it comes up heads with probability $\frac{1}{3}$. The second is weighted so that it comes up heads with probability $\frac{1}{4}$. What is the probability that when both coins are tossed, one comes up heads and the other comes up tails?
 [/INST] *

*$P(HH)=\dfrac{1}{3}\cdot\dfrac{1}{4}=\dfrac{1}{12}$

*$P(HT)=\dfrac{1}{3}\cdot\dfrac{3}{4}=\dfrac{1}{4}$

*$P(TH)=\dfrac{2}{3}\cdot\dfrac{1}{4}=\dfrac{1}{6}$

*$P(TT)=\dfrac{2}{3}\cdot\dfrac{3}{4}=\dfrac{1}{2}$
So the answer to your question is $P(HT)+P(TH)=\dfrac{1}{4}+\dfrac{1}{6}=\dfrac{5}{12}$
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