Question - Calculating Probability of Sequential Events
Solution:
To solve this probability question, we need to calculate the probability of two events happening in sequence: picking a card with the number 1 and then picking an even-numbered card after that without replacing the first card.The first event is picking a 1. There are three cards, and only one of them is a 1, so the probability of picking a 1 is:P(1) = 1/3Now, if the 1 card has been picked, there are only two cards remaining. To satisfy the second event, we need to pick an even number from the two remaining cards. There is only one even card left (either 2 or 3 was removed, depending on which was picked), so the probability of picking an even number after picking 1 is:P(even | 1) = 1/2To find the overall probability of both events occurring, we multiply the probabilities of the two events:P(1 and then even) = P(1) * P(even | 1) = (1/3) * (1/2) = 1/6The probability of picking a 1 and then picking an even number in sequence without replacement is 1/6.
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