A Jar has 9 white marbles and 6 black marbles. What is the probability of selecting a black marble, replacing it in the jar, and then selecting a white marble P(black and then white)?
The probability of selecting a black marble on the first draw is 6/15, or 2/5. Since the black marble is replaced before the second draw, the probability of selecting a white marble on the second draw is also 9/15, or 3/5. To find the probability of both events happening, we multiply their probabilities:
P(black and then white) = P(black) x P(white)
P(black and then white) = (2/5) x (3/5)
P(black and then white) = 6/25
Therefore, the probability of selecting a black marble, replacing it, and then selecting a white marble is 6/25.
To find the probability of selecting a black marble, replacing it in the jar, and then selecting a white marble, we need to multiply the individual probabilities of each event.
The probability of selecting a black marble is given by the fraction of black marbles in the total number of marbles, which is 6 out of 15. So the probability of selecting a black marble is 6/15.
After replacing the black marble back in the jar, the total number of marbles remains the same, with 9 white marbles and 6 black marbles. The probability of selecting a white marble is given by the fraction of white marbles in the total number of marbles, which is 9 out of 15. So the probability of selecting a white marble is 9/15.
To find the probability of both events happening, we multiply the probabilities together:
P(black and then white) = P(black) * P(white)
= (6/15) * (9/15)
= 54/225
= 6/25
Therefore, the probability of selecting a black marble, replacing it in the jar, and then selecting a white marble is 6/25.