Q) Bag I contains 3 black and 2 white balls, Bag II contains 2 black and 4 white balls - Maths - Probability

Question

Q) Bag I contains 3 black and 2 white balls, Bag II contains 2
black and 4 white balls A bag and a ball is selected at random
Determine the probability of selecting a black ball

Aarushi Mishra · Accepted Answer

Let us define following eventsA:Probability of choosing bag 1B:Probability of choosing bag 2C:Probability of choosing a black ballProbability of choosing bag is random
 There are two bags out of two we need to choose onePA=PB=12Bag 1 contains 3 black and 2 white ballsPC|A=35Bag 2 contains 2 black and 4 white ballsPC|B=26=13PC=PAPC|A+PBPC|B=12×35+12×13=310+16=9+530=1430=715

Q). Bag I contains 3 black and 2 white balls, Bag II contains 2 black and 4 white balls. A bag and a ball is selected at random. Determine the probability of selecting a black ball.