Question

Inger keeps her white and blqck chess pieces in separate bags. For each color, there are 8 pawns, 2 rooks, 2 bishops, 2 knights, 1 queen, and 1 king. Are the events of drawing a bishop from the bag of white pieces and then drawing the queen from the same bag dependent or independent events? Explain. Find the probability of this compound event.​

Answer 1

The events of drawing a bishop from the bag of white pieces and then drawing the queen from the same bag are dependent events. This is because the probability of drawing the queen from the bag of white pieces is affected by whether or not a bishop was drawn from the same bag.

If a bishop was drawn from the bag of white pieces, then there are only 11 pieces left in the bag, and only one of them is the queen. Therefore, the probability of drawing the queen from the bag of white pieces after a bishop has been drawn is:

P(Queen | Bishop) = 1/11

To find the probability of this compound event, we need to multiply the probabilities of the individual events:

P(Bishop and Queen) = P(Bishop) * P(Queen | Bishop)

The probability of drawing a bishop from the bag of white pieces is:

P(Bishop) = 2/15

Therefore, the probability of drawing a bishop from the bag of white pieces and then drawing the queen from the same bag is:

P(Bishop and Queen) = (2/15) * (1/11) = 2/165

So the probability of this compound event is 2/165.