Question

Box A contains 1 black and 3 white marbles, and box B contains 2 black and 4 white marbles. A box is selected at random, then a marble is drawn at random from the selected box. Given that the marble is black, find the probability that Box A was chosen.

Answer 1

Answer: Probability that Box A was chosen given that black marble is chosen is 0.5.

Step-by-step explanation:

Since we have given that

Number of boxes = 2

In Box A,

Number of black marbles = 1

Number of white marbles = 3

In Box B,

Number of black marbles = 2

Number of white marbles = 4

Since black marble is selected.

So, using Bayes theorem , we get that

$P(E_1|B)}=\dfrac{P(E_1).P(B|E_1)}{P(E_1).P(B|E_1)+P(E_2).P(E_2|B)}\\\\P(E_1|B)=\dfrac{0.5\times \dfrac{1}{3}}{0.5\dfrac{1}{3}+0.5\times \dfrac{2}{6}}\\\\P(E_1|B)}=\dfrac{0.167}{0.167+0.167}\\\\P(E_1|B)}=0.5$

Hence, probability that Box A was chosen given that black marble is chosen is 0.5.