A bag contains 9 blue, 4 black, 5 red and 7 white balls. One ball is taken out of the bag and found to be a red ball then again one ball is taken out at random from the remaining. What is the probability that it will be a white or a red ball?
Question
A bag contains 9 blue, 4 black, 5 red and 7 white balls. One ball is taken out of the bag and found to be a red ball then again one ball is taken out at random from the remaining. What is the probability that it will be a white or a red ball?
Solution
Sure, let's solve this step by step.
Step 1: First, let's calculate the total number of balls in the bag. We have 9 blue, 4 black, 5 red, and 7 white balls. So, the total number of balls is 9 + 4 + 5 + 7 = 25 balls.
Step 2: One ball is taken out and it is found to be a red ball. So, the total number of balls left in the bag is now 24 (25 - 1) and the number of red balls left is 4 (5 - 1).
Step 3: Now, we need to find the probability that the next ball taken out is either white or red. The number of favorable outcomes is the number of white balls (7) plus the number of red balls left (4). So, the number of favorable outcomes is 7 + 4 = 11.
Step 4: The probability of an event is the number of favorable outcomes divided by the total number of outcomes. So, the probability that the next ball is either white or red is 11/24.
So, the probability that the next ball taken out will be either white or red is 11/24.
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