A bag contains 5 orange pegs, 6 yellow pegs, 7 red pegs and 8 green pegs. xandrie picks 2 pegs at random from the bag to hang a pair of trousers on a washing line. determine the probability that the pegs will be of the same colour. note that these events are dependent on each other.

Question: A bag contains 5 orange pegs, 6 yellow pegs, 7 red pegs and 8 green pegs. xandrie picks 2 pegs at random from the bag to hang a pair of trousers on a washing line. determine the probability that the pegs will be of the same colour. note that these events are dependent on each other.

To calculate the probability that the two pegs Xandrie picks will be the same color, we need to consider each color individually.

Orange:

The probability of picking an orange peg on the first draw is 5/26. After the first peg is drawn, there are only 4 orange pegs left in the bag, and 25 pegs total. So, the probability of picking a second orange peg is 4/25.

Therefore, the probability of picking two orange pegs is 5/26 * 4/25 = 1/32.

Yellow:

The probability of picking a yellow peg on the first draw is 6/26. After the first peg is drawn, there are only 5 yellow pegs left in the bag, and 25 pegs total. So, the probability of picking a second yellow peg is 5/25.

Therefore, the probability of picking two yellow pegs is 6/26 * 5/25 = 3/50.

Red:

The probability of picking a red peg on the first draw is 7/26. After the first peg is drawn, there are only 6 red pegs left in the bag, and 25 pegs total. So, the probability of picking a second red peg is 6/25.

Therefore, the probability of picking two red pegs is 7/26 * 6/25 = 21/130.

Green:

The probability of picking a green peg on the first draw is 8/26. After the first peg is drawn, there are only 7 green pegs left in the bag, and 25 pegs total. So, the probability of picking a second green peg is 7/25.

Therefore, the probability of picking two green pegs is 8/26 * 7/25 = 28/130.

To find the overall probability of picking two pegs of the same color, we need to add up the probabilities for each color:

1/32 + 3/50 + 21/130 + 28/130 = 53/130

Therefore, the probability that Xandrie will pick two pegs of the same color is 53/130.

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