Box contains 4 white balls and 8 black balls. Pick a ball with your left hand, and don't look, pick a ball with your right hand, and don't look at it either.

a. what is the probability the ball in your left hand is white?

b. Next, you look at the ball in your right hand and it is black. Now what is the probability that the ball in your left hand is white?

I figured it out never mind.

a. is 1/3 because 4 of 12 balls are white, you pick with your left hand first, so all balls are still there.

b. 1 ball is gone, so there are 4 white 7 black, therefore 11 balls left. 4/11 is the probability that the ball in your left is white.

a) .... prob(white) = 4/12 = 1/3


b) ... prob(white in left) = 4/11

A 1/3

B. 4/11

To solve this problem, we first need to understand the total number of possible outcomes and the number of desired outcomes. Let's go step by step.

a. Probability of picking a white ball with your left hand:
- Total number of balls in the box: 4 white + 8 black = 12 balls
- Total number of outcomes: 12 balls

Since the number of desired outcomes is the number of white balls (4) and the number of total outcomes is the total number of balls (12), the probability of picking a white ball with your left hand is 4/12, which can be simplified to 1/3.

b. After picking a black ball with your right hand, the situation has changed. Now, we know the outcome of one ball, so we need to calculate the probability based on this knowledge.

- Total number of balls remaining in the box: 11 balls (since you picked one with your right hand and know its color)
- Number of white balls remaining in the box: 4 white balls (since the color of the ball in your left hand is unknown)
- Number of black balls remaining in the box: 7 black balls (since one black ball was revealed by picking it with your right hand)

Now, we can calculate the probability of the ball in your left hand being white, given the information that the ball in your right hand is black.

- Total number of remaining outcomes: 11 balls
- Number of desired outcomes (picking a white ball with your left hand, given the black ball in your right hand): 4 white balls

Therefore, the probability of the ball in your left hand being white, given that the ball in your right hand is black, is 4/11.