Jar A contains 6 red balls and 4 white balls. Jar B contains 7 red balls and 2 white balls. You randomly select one ball from Jar A and, without knowing it’s color, drop it into Jar B. You then randomly select one ball from Jar B. What is the probability that the ball you select from Jar B will be red?
* is it 6/10?
To find the probability of selecting a red ball from Jar B after transferring a ball from Jar A, we need to calculate the combined probability of two events: selecting a red ball from Jar A and selecting a red ball from Jar B.
First, let's calculate the probability of selecting a red ball from Jar A. Jar A contains a total of 6 red balls and 4 white balls, so the probability of selecting a red ball from Jar A is 6/10.
Next, we need to determine the probability of selecting a red ball from Jar B given that a ball has been transferred from Jar A. After transferring a ball from Jar A to Jar B, the total number of balls in Jar B becomes 11 (7 red balls from Jar B + 6 balls transferred from Jar A - assuming the transferred ball is red).
Since we don't know the color of the transferred ball, we consider both possibilities: red or white. If the transferred ball is red, then there would be a total of 8 red balls in Jar B (7 red balls from Jar B + 1 red ball transferred from Jar A). Therefore, the probability of selecting a red ball from Jar B, assuming the transferred ball is red, is 8/11.
Now, if the transferred ball is white, then there would still be a total of 7 red balls in Jar B (7 red balls from Jar B). The probability of selecting a red ball from Jar B, assuming the transferred ball is white, is 7/11.
To calculate the overall probability of selecting a red ball from Jar B after transferring a ball from Jar A, we need to consider the probabilities for both possible scenarios and take their weighted average.
Probability that the transferred ball is red: (Probability of selecting a red ball from Jar A) * (Probability of selecting a red ball from Jar B, assuming the transferred ball is red) = (6/10) * (8/11)
Probability that the transferred ball is white: (Probability of selecting a red ball from Jar A) * (Probability of selecting a red ball from Jar B, assuming the transferred ball is white) = (6/10) * (7/11)
Let's calculate the final probability by taking the sum of these two probabilities:
(6/10) * (8/11) + (6/10) * (7/11) = 48/110 + 42/110 = 90/110 = 9/11
Therefore, the probability of selecting a red ball from Jar B is 9/11 or approximately 0.818 (rounded to three decimal places).
So, the answer is not 6/10. The correct probability is 9/11.
To determine the probability that the ball you select from Jar B will be red, let's break down the steps:
Step 1: Calculate the probability of selecting a red ball from Jar A.
In Jar A, there are a total of 4 + 6 = 10 balls.
Since there are 6 red balls in Jar A, the probability of selecting a red ball from Jar A is 6/10 or 3/5.
Step 2: Calculate the probability of selecting the ball you transferred, which has an unknown color.
Since the ball you transferred from Jar A to Jar B could be either red or white, the probability of selecting this ball is 1.
Step 3: Calculate the probability of selecting a red ball from Jar B, considering the transferred ball.
In Jar B, there are now a total of 2 + 7 + 1 = 10 balls, taking into account the transferred ball.
Since there are now 7 red balls in Jar B, the probability of selecting a red ball from Jar B is 7/10.
Thus, the probability that the ball you select from Jar B will be red is (3/5) * (7/10) = 21/50, which is approximately 0.42 or 42%.