Did you know?
Did you know that the probability of choosing two black balls from a bag with 3 black balls and 2 white balls is determined by multiplying the probabilities? For (a), the probability of selecting a black ball is 3/5, and since the ball is replaced, the probability of choosing another black ball is also 3/5. Therefore, the probability of choosing two black balls is (3/5) x (3/5) = 9/25.
In the case of (b), the probability of selecting a black ball is still 3/5, but now the probability of selecting a white ball is 2/5. To find the probability of choosing one black and one white, we multiply these probabilities and multiply by 2 (since we can have black-white or white-black). Hence, (3/5) x (2/5) x 2 = 12/25.
Lastly, for (c) "at least one is black," we can calculate the probability of the opposite event (neither ball is black) and subtract it from 1. The probability of not choosing a black ball for the first pick is 2/5, and not choosing a black ball for the second pick (given that the first pick was not black) is also 2/5. Multiplying these probabilities, we obtain (2/5) x (2/5) = 4/25 for the probability of selecting no black balls. Since the opposite event "at least one is black" is the complement event, we get the probability of at least one black ball to be 1 - 4/25 = 21/25.
Understanding these probabilities can provide insights into the likelihood of different outcomes when drawing balls from a bag.
