A bag contains sixteen white balls and fourteen red balls. Two balls are drawn consecutively without replacement. What is the probability that both balls are white?
Since this is an and probability, we will be multiplying probabilities together. It’s also important to pay attention to the fact that this is without replacement, meaning once you take one of the balls out, you do not replace it for the next time that you take one out. So we will be consecutively, so in a row, drawing these balls out of the bag. So for the first ball that we will be taking out of the bag, there are sixteen white. So sixteen white balls out of a total of thirty because sixteen white balls plus fourteen red balls would be thirty.
So the probability of drawing a white ball the very first time would be sixteen out of thirty. Now, our second time that we draw, there are no longer sixteen white balls because we already took one out because it’s the probability that both of the balls are white. So we’re assuming on that first draw, we will be getting a white one. So now instead of sixteen, it would be fifteen white balls to choose from. And the total will actually be different as well because out of the thirty balls, we drew one out and it’s gone. So now instead of thirty, there are twenty-nine.
So we have sixteen thirtieths times fifteen twenty-ninths, which is two hundred and forty out of eight hundred and seventy. And we’ve reduced, both numbers are divisible by thirty. And we get eight twenty-ninths.
So the probability that both balls are white is eight out of twenty-nine.