A box contains 4 purple and 9 yellow balls.We take out 2 balls (with replacement). What is the probability of drawing a second ball yellow, if the first ball was purple? please sovle in details..thanks
You still have the probability of 9/13 in drawing a yellow ball.
To find the probability of drawing a second yellow ball, given that the first ball drawn was purple, we can use the concept of conditional probability.
Step 1: Determine the Probability of Drawing a Purple Ball
The box contains a total of 4 purple and 9 yellow balls, so the probability of drawing a purple ball initially can be calculated as:
P(Purple) = Number of Purple Balls / Total Number of Balls
P(Purple) = 4 / (4 + 9) = 4/13
Step 2: Determine the Probability of Drawing a Yellow Ball After the First Ball is Purple
Since the first ball is replaced, the total number of balls remains the same. Now, we need to find the probability of drawing a yellow ball after the first ball was purple. Since the first ball was put back into the box, the new sample space still contains 4 purple and 9 yellow balls. Therefore, the probability of drawing a yellow ball after the first ball was purple can be calculated as:
P(Yellow|Purple) = Number of Yellow Balls / Total Number of Balls
P(Yellow|Purple) = 9 / (4 + 9) = 9/13
So, the probability of drawing a second yellow ball, given that the first ball was purple, is 9/13.