Suppose a bag contains 7 red chips, 8 black chips, and 3 green chips. You draw two chips (without replacement) from the bag. Find the probability that you drew a red chip first and then a black chip second.
Red = 7/18
Black = 8/17
To find the probability that both (all) events would occur, multiply the probabilities of the individual events.
To find the probability that you drew a red chip first and then a black chip second, we need to calculate the probability of drawing a red chip first and then multiplying it by the probability of drawing a black chip second, given that the first chip was red.
First, let's calculate the probability of drawing a red chip as the first chip.
Total number of chips = 7 (red) + 8 (black) + 3 (green) = 18
Since we draw without replacement, after drawing the first chip, there will be 17 chips left in the bag.
Probability of drawing a red chip first = Number of red chips / Total number of chips
= 7 / 18
Next, let's calculate the probability of drawing a black chip as the second chip, given that the first chip was red.
After drawing the red chip, there will be 6 red chips left and 8 black chips remaining in the bag. The total number of chips remaining will now be 17 - 1 = 16.
Probability of drawing a black chip second, given that the first chip was red = Number of black chips remaining / Total number of chips remaining
= 8 / 16
= 1 / 2
Finally, we can find the probability of drawing a red chip first and then a black chip second by multiplying the probabilities:
Probability (Red first, Black second) = Probability of drawing a red chip first * Probability of drawing a black chip second, given that the first chip was red
= (7/18) * (1/2)
= 7/36
Therefore, the probability of drawing a red chip first and then a black chip second is 7/36.