Question - Probability of Selecting a Pencil and a Color Pencil from Two Boxes
Solution:
The image shows a probability problem that reads:"A box contains 6 plain pencils and 4 pens. A second box contains 3 color pencils and 7 crayons. One item from each box is chosen at random. What is the probability that a plain pencil from the first box and a color pencil from the second box are selected?"To solve this, we need to calculate the probability that each of these two independent events occurs and then multiply these probabilities together.Probability of selecting a plain pencil from the first box:There are 6 plain pencils out of a total of 6 plain pencils + 4 pens = 10 items in the first box.So the probability, P(plain pencil), is 6/10, which simplifies to 3/5.Probability of selecting a color pencil from the second box:There are 3 color pencils out of a total of 3 color pencils + 7 crayons = 10 items in the second box.So the probability, P(color pencil), is 3/10.Since these two events are independent, we multiply the two probabilities together to get the combined probability:P(plain pencil and color pencil) = P(plain pencil) * P(color pencil) = (3/5) * (3/10) = 9/50.Therefore, the probability that a plain pencil from the first box and a color pencil from the second box are selected is 9/50.
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