Question

Emily keeps her white and black chess pieces in separate bags for each color. There are eight pawns, 2 bishops, two nights, one queen and one king. Are the events of drawing a night from the bag of white pieces and trying a pan from the bag of black pieces dependent or independent events? explain. find the probability of this compound event

Answer 1

Drawing a knight from the white pieces and a pawn from the black pieces are independent events, and the probability of the compound event is 1/16.

Step-by-step explanation:

The question is whether the events of drawing a knight from the bag of white chess pieces and drawing a pawn from the bag of black chess pieces are independent or dependent events.

By definition, two events are independent if the occurrence of one does not affect the probability of the occurrence of the other. In this case, drawing a piece from one bag does not in any way affect the outcome of a draw from a separate bag. Therefore, these two events are independent.

The probability of the compound event, which is the probability of both drawing a knight from the bag of white chess pieces and a pawn from the bag of black chess pieces, can be found by multiplying the probabilities of the two independent events.

Since there are two knights and 16 total pieces in the white bag, the probability of drawing a knight is 2/16 or 1/8.

Similarly, there are eight pawns in the black bag out of 16 pieces, so the probability of drawing a pawn is 8/16 or 1/2. Multiplying these probabilities gives us 1/8 * 1/2 = 1/16 as the probability of the compound event.