Question

a bag contains 5 balls. two balls are drawn at random and were found to be red. find the probability that a) all the balls left in the bag are red ii) no red ball is left in the bag iii) only one red ball is left in the bag?

Answer 1

The probabilities of whether all balls left in the bag are red, no red balls are left, or only one red ball is left after two red balls have been drawn, depend on the initial number of red and non-red balls in the bag, which is not specified in the question.

Step-by-step explanation:

The question involves the calculation of conditional probabilities when balls are drawn from a bag without replacement. In the scenario given, two balls have already been drawn and they are both red. We need to calculate the probabilities for the different possible contents of the bag after these draws.

To calculate these probabilities, we would generally use the total number of possible outcomes and the number of favorable outcomes for the event in question. Since not enough information is given about the total composition of the bag, we can't provide the exact probabilities. For instructional purposes, we will assume that there were initially x red balls and y non-red balls, with x + y = 5 before any balls were drawn.

Let's consider the cases:

1. All the balls left in the bag are red: After drawing 2 red balls, the probability that the remaining balls in the bag are all red depends on the initial number of red balls. If there were initially 4 or 5 red balls, then this would be possible.
2. No red ball is left in the bag: If we assume there were only 2 red balls to begin with, after drawing them, no red ball would be left.
3. Only one red ball is left in the bag: This would occur if there were initially 3 red balls in the bag.

Without the exact initial composition of the bag, we can't provide numerical probabilities. However, we can say that the probabilities depend on the initial number of red and non-red balls present.