Question - Probability Calculation: Picking Even Number and 8
Solution:
The problem in the image is asking us to calculate the probability of picking an even number and then picking an 8 when selecting from the cards labeled 7, 8, and 9.Firstly, let's determine the probability of picking an even number from the cards. Since there is only one even number (which is 8) out of three cards, the probability of picking an even number at the first try is 1/3.Since the card is put back after the first pick, the sample space does not change, and each pick is independent of the other.Next, we need to determine the probability of picking an 8. Well, because we replaced the card after the first pick, the probability of picking an 8 on the second pick is also 1/3.To find the overall probability of these two independent events happening one after the other (picking an even number and then picking an 8), we need to multiply the probabilities of each event occurring:Probability of picking an even number * Probability of picking an 8 = (1/3) * (1/3) = 1/9.So the probability of picking an even number and then picking an 8 in this scenario is 1/9.
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