Lorenzo has a jar with 21 green olives and 15 black olives in it. If he takes two olives out of the jae with replacement,what is the probability that the first olive will be black and the second olive will be green?
Since he puts the olives back, the second result is independent of the first
prob(black,green) = (15/36)(21/36) = 35/144
you suck
To find the probability of drawing a black olive followed by a green olive with replacement, we need to consider the total number of olives and the number of black and green olives.
Total number of olives: 21 green olives + 15 black olives = 36 olives
Probability of drawing a black olive on the first draw: Number of black olives / Total number of olives = 15 / 36
Since we are replacing the olive before the second draw, the total number of olives remains the same.
Probability of drawing a green olive on the second draw: Number of green olives / Total number of olives = 21 / 36
To find the combined probability, we multiply the two probabilities together:
Probability = (15 / 36) * (21 / 36)
Now we can calculate this probability:
To find the probability of selecting a black olive followed by a green olive, we need to determine the probability of each event separately and then multiply them together.
First, let's determine the probability of selecting a black olive on the first try. The total number of olives in the jar is 21 green + 15 black = 36 olives. Out of these, there are 15 black olives. Therefore, the probability of selecting a black olive on the first try is 15/36.
Next, let's determine the probability of selecting a green olive on the second try, while assuming the first olive was replaced back into the jar. After the first olive is put back, the total number of olives in the jar remains the same, i.e., 21 green + 15 black = 36 olives. However, since the first olive was replaced, the number of green olives and black olives also remains the same. So, we still have 21 green olives out of 36 remaining olives. Therefore, the probability of selecting a green olive on the second try is 21/36.
Finally, we need to multiply the probabilities together to get the probability of both events happening. So,
Probability = (Probability of black on the first try) * (Probability of green on the second try)
= (15/36) * (21/36)
= 315/1296
= 35/144
Therefore, the probability that the first olive will be black and the second olive will be green is 35/144 or approximately 0.2431.