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Home » Suppose we have four boxes A, B, C and D containing coloured marbles as given below: One of the boxes has been selected at random and a single marble is drawn from it. If the marble is red, what is the probability that it was drawn from box ?, box B?, box C?
Suppose we have four boxes A, B, C and D containing coloured marbles as given below: One of the boxes has been selected at random and a single marble is drawn from it. If the marble is red, what is the probability that it was drawn from box A ?, box B?, box C?
CBSE | Class 12 | Maths | NCERT | Probability
Suppose we have four boxes A, B, C and D containing coloured marbles as given below: One of the boxes has been selected at random and a single marble is drawn from it. If the marble is red, what is the probability that it was drawn from box A ?, box B?, box C?

Solution:

Let us assume R be the event of drawing the red marbles
Let us additionally assume that the letters E_{A}, E_{B} and E_{c} denote the boxes A, B and C respectively

Given that,

Total number of marbles =40

Also, total number of red marbles =15

P(R)=15 / 40

=3 / 8

Probability of taking out the red marble from box A,

P\left(E_{A} \mid R\right)=\frac{P\left(E_{A} \cap R\right)}{P(R)}

=\frac{\frac{1}{40}}{3}

=1 / 15

Also, probability of taking out the red marble from box B,

P\left(E_{B} \mid R\right)=\frac{P\left(E_{B} \cap R\right)}{P(R)}

=\frac{\frac{6}{40}}{3}

=2 / 5

And, Probability of taking out the red marble from box \mathrm{C},

P\left(E_{C} \mid R\right)=\frac{P\left(E_{C} \cap R\right)}{P(R)}

=\frac{\frac{8}{40}}{3}

=8 / 15

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