To solve this problem, we need to use the law of total probability. The law of total probability states that the probability of an event can be found by considering all the different ways the event could occur.

Step 1: Calculate the probability of selecting each bag. Since one bag is selected at random, the probability of selecting each bag is 1/2.

Step 2: Calculate the probability of drawing a red ball from each bag. In the first bag, there are 4 red balls out of a total of 7 balls, so the probability is 4/7. In the second bag, there are 2 red balls out of a total of 6 balls, so the probability is 2/6 or 1/3.

Step 3: Use the law of total probability to find the overall probability of drawing a red ball. This is done by multiplying the probability of selecting each bag by the probability of drawing a red ball from that bag, and then adding these values together.

So, the overall probability of drawing a red ball is (1/2 * 4/7) + (1/2 * 1/3) = 2/7 + 1/6 = 12/42 + 7/42 = 19/42.

So, the correct answer is 19/42.

Question

To solve this problem, we need to use the law of total probability. The law of total probability states that the probability of an event can be found by considering all the different ways the event could occur.

Step 1: Calculate the probability of selecting each bag. Since one bag is selected at random, the probability of selecting each bag is 1/2.

Step 2: Calculate the probability of drawing a red ball from each bag. In the first bag, there are 4 red balls out of a total of 7 balls, so the probability is 4/7. In the second bag, there are 2 red balls out of a total of 6 balls, so the probability is 2/6 or 1/3.

Step 3: Use the law of total probability to find the overall probability of drawing a red ball. This is done by multiplying the probability of selecting each bag by the probability of drawing a red ball from that bag, and then adding these values together.

So, the overall probability of drawing a red ball is (1/2 * 4/7) + (1/2 * 1/3) = 2/7 + 1/6 = 12/42 + 7/42 = 19/42.

So, the correct answer is 19/42.

Knowee AI · Accepted Answer

To solve this problem, we need to use the law of total probability. The law of total probability states that the probability of an event can be found by considering all the different ways the event could occur.

Step 1: Calculate the probability of selecting each bag. Since one bag is selected at random, the probability of selecting each bag is 1/2.

Step 2: Calculate the probability of drawing a red ball from each bag. In the first bag, there are 4 red balls out of a total of 7 balls, so the probability is 4/7. In the second bag, there are 2 red balls out of a total of 6 balls, so the probability is 2/6 or 1/3.

Step 3: Use the law of total probability to find the overall probability of drawing a red ball. This is done by multiplying the probability of selecting each bag by the probability of drawing a red ball from that bag, and then adding these values together.

So, the overall probability of drawing a red ball is (1/2 * 4/7) + (1/2 * 1/3) = 2/7 + 1/6 = 12/42 + 7/42 = 19/42.

So, the correct answer is 19/42.

A bag contains 4 red and 3 black balls. A second bag contains 2 red and 4 black balls. One bag is selected at random. From the selected bag, one ball is drawn. Find the probability that the ball drawn is red.Choices:- 23/42 19/42 7/32 16/39

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