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Tasya [4]
3 years ago
13

a jar contains 5 blue marbles and 3 red marbles. suppose you choose a marble at random and do not replace it. then choose a seco

nd marble. find the probability of the following event. both of the selected marbles are red.
Mathematics
1 answer:
lina2011 [118]3 years ago
4 0
\mathbb P(R_1\cap R_2)=\mathbb P(R_2\mid R_1)\mathbb P(R_1)

The probability of drawing a red marble on the first attempt is

\mathbb P(R_1)=\dfrac{\dbinom31}{\dbinom51}=\dfrac35

After the first marble is drawn, and we know it to be red, we're drawing the next marble from a pool with one less marble than before (i.e. conditioning on the event R_1). So

\mathbb P(R_2\mid R_1)=\dfrac{\dbinom21}{\dbinom71}=\dfrac27

And so

\mathbb P(R_1\cap R_2)=\dfrac35\cdot\dfrac27=\dfrac6{35}
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