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A bag contains 3 red and 7 black balls, ...

A bag contains 3 red and 7 black balls, two balls are taken out at random, without replacement, If the first ball taken out is red, then the probability that the second taken out red ball is

A

`1/10`

B

`1/15`

C

`3/10`

D

`2/21`

Text Solution

AI Generated Solution

The correct Answer is:
To find the probability that the second ball drawn is red given that the first ball drawn was red, we can follow these steps: ### Step 1: Identify the total number of balls We have a total of 3 red balls and 7 black balls in the bag. **Total number of balls = 3 (red) + 7 (black) = 10 balls.** **Hint:** Always start by determining the total number of items in the scenario. ### Step 2: Determine the outcome of the first draw Since we are given that the first ball drawn is red, we now have: - 2 red balls left (since one red ball has been drawn) - 7 black balls still in the bag **Total number of balls remaining = 2 (red) + 7 (black) = 9 balls.** **Hint:** After the first draw, adjust the counts of the remaining items accordingly. ### Step 3: Calculate the probability of drawing a red ball second Now, we need to find the probability that the second ball drawn is red. There are 2 red balls remaining out of a total of 9 balls. **Probability of drawing a red ball second = Number of red balls remaining / Total balls remaining = 2 / 9.** **Hint:** The probability of an event is calculated as the number of favorable outcomes divided by the total number of possible outcomes. ### Final Answer The probability that the second ball drawn is red, given that the first ball drawn was red, is **2/9**. ---
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