Bag A contains 6 white beads and 3 black beads. Bag B contains 6 white beads and 4 black beads.One bead is chosen at random from each bag. find the probability that both beads are black and at least one of the two beads is white??
It would help if you proofread your questions before you posted them. "And" indicates both of these are occurring, but this would be impossible with the situation you describe.
Probability of both/all events occurring is found by multiplying the probabilities of the individual events.
Both black = 3/9 * 4/10 = ?
"At least one of the two beads is white" means either one white bead or two white beads.
Either-or probabilities are found by adding the individual probabilities.
One bead white = 6/9 * 4/10 or 3/9 * 6/10
Two white beads = 6/9 * 6/10 = ?
To find the probability that both beads are black and at least one of the two beads is white, we can use the principle of complementary probability.
Step 1: Determine the probability that both beads are black.
In bag A, we have a total of 9 beads (6 white + 3 black). Therefore, the probability of choosing a black bead from bag A is 3/9.
In bag B, we have a total of 10 beads (6 white + 4 black). Therefore, the probability of choosing a black bead from bag B is 4/10.
To find the probability that both beads are black, we need to multiply the two probabilities:
P(both black) = (3/9) * (4/10) = 12/90 = 2/15
Step 2: Find the probability that at least one of the two beads is white.
To find the probability that at least one of the two beads is white, we can subtract the probability that both beads are black from 1.
P(at least one white) = 1 - P(both black)
= 1 - 2/15
= 13/15
Therefore, the probability that both beads are black and at least one of the two beads is white is 13/15.
To find the probability that both beads are black and at least one of the two beads is white, we can apply the principle of conditional probability.
First, let's find the individual probabilities for choosing a black bead from each bag:
In Bag A, the probability of picking a black bead is 3/9 since there are 3 black beads out of a total of 9 beads.
In Bag B, the probability of picking a black bead is 4/10 since there are 4 black beads out of a total of 10 beads.
Next, let's find the probability of picking at least one white bead:
We can do this by finding the probability of the complementary event, which is picking no white bead at all. This can happen when we pick two black beads.
The probability of picking two black beads from Bag A and Bag B can be calculated by multiplying the probabilities of picking a black bead from each bag:
P(Two black beads) = P(black from Bag A) * P(black from Bag B)
= (3/9) * (4/10)
= 12/90
= 2/15
Therefore, the probability of picking at least one white bead is the complement of picking two black beads:
P(At least one white bead) = 1 - P(Two black beads)
= 1 - 2/15
= 13/15
So, the probability that both beads are black and at least one of the two beads is white is 13/15.