 # In a box there are 16 ice-creams: 6 lemon flavor,4 mint flavor and 6 strawberry flavor.When we extra Bruno Pittman 2022-07-01 Answered
In a box there are 16 ice-creams: 6 lemon flavor,4 mint flavor and 6 strawberry flavor.When we extract two ice-creams,what's the probability of getting two different flavors,given that at least one is strawberry flavor.
That's my solution :
$P\left(A\right)$ = "Different flavors" = $\frac{\left(\genfrac{}{}{0}{}{16}{2}\right)}{16!}$
$P\left({B}^{c}\right)$ = "At least one is strawberry flavor" = $1-\frac{\left(\genfrac{}{}{0}{}{10}{2}\right)}{16!}$
We want $P\left(A|{B}^{c}\right)$ using conditional probability, where I go wrong?
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Assuming that each ice-cream has the same probability of being drawn, you could compute it as the ratio of the ways of getting
(one strawberry, one other) / (one strawberry, one other + two strawberries)
$\frac{\left(\genfrac{}{}{0}{}{6}{1}\right)\left(\genfrac{}{}{0}{}{10}{1}\right)}{\left(\genfrac{}{}{0}{}{6}{1}\right)\left(\genfrac{}{}{0}{}{10}{1}\right)+\left(\genfrac{}{}{0}{}{6}{2}\right)}$

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