MATH SOLVE

3 months ago

Q:
# 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.

Accepted Solution

A:

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 = 2In Box A, Number of black marbles = 1Number of white marbles = 3In Box B,Number of black marbles = 2Number of white marbles = 4Since black marble is selected.So, using Bayes theorem , we get that [tex]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[/tex]Hence, probability that Box A was chosen given that black marble is chosen is 0.5.