two boxes are selected randomly.the first box contains 2 white balls and 3 black balls.the second ball contains 3 white balls and 4 black balls.what is the probability of drawing a white ball?
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Assuming that the pick is either one box or the other "ball," either-or probabilities are found by adding the individual probabilities.
2/5 + 3/7 = ?
To find the probability of drawing a white ball, we need to consider the total number of balls and the number of white balls in each box.
Let's calculate the probability for each box separately and then combine them using the law of total probability.
Box 1:
Total number of balls in box 1 = 2 white + 3 black = 5
Probability of drawing a white ball from box 1 = Number of white balls in box 1 / Total number of balls in box 1 = 2/5
Box 2:
Total number of balls in box 2 = 3 white + 4 black = 7
Probability of drawing a white ball from box 2 = Number of white balls in box 2 / Total number of balls in box 2 = 3/7
Now, let's use the Law of Total Probability to combine the probabilities of drawing a white ball from each box.
Assuming both boxes are equally likely to be selected, the probability of selecting box 1 (P(Box 1)) = 1/2
The probability of selecting box 2 (P(Box 2)) = 1/2
The total probability of drawing a white ball is given by:
Probability of drawing a white ball = P(Box 1) * Probability of drawing a white ball from box 1 + P(Box 2) * Probability of drawing a white ball from box 2
Probability of drawing a white ball = (1/2) * (2/5) + (1/2) * (3/7)
Probability of drawing a white ball = 1/5 + 3/14
Probability of drawing a white ball = (14/70) + (15/70)
Probability of drawing a white ball = 29/70
Therefore, the probability of drawing a white ball is 29/70.