A box contains two black balls and three gold balls. Two
balls are randomly drawn in succession from the box.
a. If there is no replacement, what is the probability
that both balls are black?
b. If there is replacement before the second draw, what
is the probability that both balls are black?
What is your thinking here?
What do you mean?
I will be happy to critique your thinking, but reluctant to do it for you.
I am not understanding this at all!!! I have read over my material for this class & I still don't get it!! Can someone PLEASE help me?!!!!?????
Look into the text book and search for pobability in box array. create one and then give the answers
To solve this problem, we need to understand the concept of probability and combinations.
a. If there is no replacement, the probability of drawing a black ball on the first draw is 2/5 because there are 2 black balls out of a total of 5 balls in the box. After the first draw, there will be one less ball in the box, so on the second draw, the probability of drawing another black ball is 1/4. Since we want to find the probability of both balls being black, we need to multiply the probabilities of both events happening:
Probability (both balls are black) = (2/5) * (1/4) = 2/20 = 1/10
So, the probability that both balls are black, without replacement, is 1/10.
b. If there is replacement before the second draw, it means that after the first ball is drawn, it is placed back into the box, so the total number of balls remains the same. In this case, the probability of drawing a black ball on each draw is still 2/5 because the proportion of black balls to the total number of balls does not change. Since the draws are independent events, we can once again multiply the probabilities:
Probability (both balls are black with replacement) = (2/5) * (2/5) = 4/25
So, the probability that both balls are black, with replacement, is 4/25.