are the events of drawing a knight from the bag of white pieces and drawing a pawn from the bag of black pieces dependent or independent events? find the probability of this compound event.
Independent
(number of white knights/number of white pieces) * (number of black pawns/number of black pieces)
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To determine whether two events are dependent or independent, we need to consider whether the outcome of one event affects the outcome of the other event.
In this case, drawing a knight from the bag of white pieces and drawing a pawn from the bag of black pieces are independent events. The reason is that the color of the piece (white or black) in one bag does not affect the color of the piece drawn from the other bag.
To find the probability of this compound event, we need to calculate the individual probabilities of each event and then multiply them together.
Let's assume that the bag of white pieces contains 10 knights and the bag of black pieces contains 20 pawns.
The probability of drawing a knight from the bag of white pieces is given by:
Probability of drawing a knight = Number of knights / Total number of pieces in the bag
= 10 / (10 + 20)
= 10 / 30
= 1/3
Similarly, the probability of drawing a pawn from the bag of black pieces is:
Probability of drawing a pawn = Number of pawns / Total number of pieces in the bag
= 20 / (10 + 20)
= 20 / 30
= 2/3
To find the probability of the compound event (drawing a knight from the bag of white pieces and a pawn from the bag of black pieces), we multiply the individual probabilities together:
Probability of compound event = Probability of drawing a knight * Probability of drawing a pawn
= (1/3) * (2/3)
= 2/9
Therefore, the probability of drawing a knight from the bag of white pieces and a pawn from the bag of black pieces is 2/9.