Question - Calculating Probability of Events Happening Successively
Solution:
To solve this probability question, we need to calculate the probability of two independent events happening one after the other:1. Picking an even number.2. Picking an 8.Since the card is put back after the first pick, the two events are independent, and we can calculate the probability of each event separately and then multiply them.First, let's find the probability of picking an even number from the cards shown. There are three cards, and only one of them is even (the 8). So the probability of picking an even number is:P(even) = Number of even cards / Total number of cards = 1/3Next, let's find the probability of picking an 8. Since the card is put back after the first draw, the probability remains the same for picking an 8:P(8) = Number of cards with 8 / Total number of cards = 1/3Now we multiply the probabilities of the two independent events:P(even, then 8) = P(even) * P(8) = (1/3) * (1/3) = 1/9So, the probability of picking an even number and then picking an 8, with replacement, is 1/9.
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