A bag contains red and blue marbles. Two marbles are drawn without
replacement. The probability of selecting a red marble and then a blue marble is 0
.28.
The probability of selecting a red marble on the first draw is 0.5. What is the probability
of selecting a blue marble on the second draw, given that the first marble drawn was
red?
If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.
.5 * B = .28
Solve for B.
0.75
assignment
To find the probability of selecting a blue marble on the second draw, given that the first marble drawn was red, we can use conditional probability.
Conditional probability is the probability of an event occurring given that another event has already occurred. In this case, we want to find the probability of selecting a blue marble on the second draw, given that the first marble drawn was red.
The notation for conditional probability is P(B|A), which represents the probability of event B occurring given that event A has already occurred.
In this case, event A is drawing a red marble on the first draw, and event B is drawing a blue marble on the second draw.
Given that the probability of selecting a red marble on the first draw is 0.5, we can assume that there are equal numbers of red and blue marbles in the bag.
Let's proceed with the calculation using the formula for conditional probability:
P(B|A) = P(A and B) / P(A)
We know that P(A and B) is given as 0.28, and P(A) is given as 0.5.
Plugging these values into the formula, we have:
P(B|A) = 0.28 / 0.5
Simplifying the expression, we get:
P(B|A) = 0.56
Therefore, the probability of selecting a blue marble on the second draw, given that the first marble drawn was red, is 0.56 or 56%.