Question

A bag holds 11 beads. 7 of the beads are red. The rest are white. Two beads are taken from the bag at random. Work out the probability that one bead of each color is taken. You must show your working out.

Answer 1

The probability of drawing one red and one white bead from the bag is 28/55. This is found by considering both possible orders of drawing the beads and adding the probabilities of each scenario.

Step-by-step explanation:

To calculate the probability that one red and one white bead are taken from the bag, we need to consider the two possible scenarios:

1. A red bead is drawn first followed by a white bead.
2. A white bead is drawn first followed by a red bead.

For scenario 1, the probability of drawing a red bead first is 7/11, since there are 7 red beads out of 11 total. The probability of then drawing a white bead is 4/10, because after removing a red bead there are 4 white beads left out of the remaining 10 beads in the bag.

For scenario 2, the probability of drawing a white bead first is 4/11, followed by the probability of drawing a red bead which is 7/10 since there are still 7 red beads out of the 10 remaining.

To get the total probability of drawing one bead of each color, we add the probabilities of the two scenarios:

(7/11) × (4/10) + (4/11) × (7/10) = 28/110 + 28/110 = 56/110, which simplifies to 28/55.

The final probability of drawing one red and one white bead is 28/55.