There is a stack of 8 cards, each given a different number from 1 to 8. Suppose we select a card randomly from the stack, replace it, and then randomly select another card. What is the probability that the first card is an even number and the second card is less than 4?Write your answer as a fraction in simplest form.
Question
There is a stack of 8 cards, each given a different number from 1 to 8. Suppose we select a card randomly from the stack, replace it, and then randomly select another card. What is the probability that the first card is an even number and the second card is less than 4?Write your answer as a fraction in simplest form.
Solution
To solve this problem, we need to understand that these are two independent events, meaning that the outcome of the first event does not affect the outcome of the second event.
Step 1: Determine the probability of the first event. The first event is selecting an even number. The even numbers from 1 to 8 are 2, 4, 6, and 8. So, there are 4 favorable outcomes. Since there are 8 possible outcomes in total (the numbers 1 to 8), the probability of the first event is 4/8 or 1/2.
Step 2: Determine the probability of the second event. The second event is selecting a number less than 4. The numbers less than 4 are 1, 2, and 3. So, there are 3 favorable outcomes. Again, since there are 8 possible outcomes in total, the probability of the second event is 3/8.
Step 3: Since these are independent events, the probability of both events occurring is the product of their individual probabilities. So, the probability that the first card is an even number and the second card is less than 4 is (1/2) * (3/8) = 3/16.
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