Question

Ten cards numbered 1 to 10 are placed in a box, mixed up thoroughly and then one card is drawn randomly. If it is known that the number on the drawn card is more than 3, what is the probability that it is an even number?

Hint:

When dealing with conditional probability, always adjust the total number of possible outcomes based on the given condition.

Answer 1

Step 1: Understanding the situation.
The total number of cards is 10, numbered from 1 to 10. The probability is conditional on the fact that the drawn card is more than 3. Therefore, we are only concerned with the cards numbered 4 through 10.

Step 2: Finding the favorable outcomes.
The even numbers greater than 3 are 4, 6, 8, and 10. So, the favorable outcomes are 4, 6, 8, and 10, which are 4 even numbers.

Step 3: Finding the total possible outcomes.
The cards greater than 3 are numbered 4, 5, 6, 7, 8, 9, and 10, giving us a total of 7 possible outcomes.

Step 4: Calculating the probability.
The probability that the card drawn is even given that it is greater than 3 is the ratio of favorable outcomes to total outcomes: \[ P(\text{even} \mid \text{card} > 3) = \frac{4}{7}. \]

Step 5: Conclusion.
Thus, the probability that the card drawn is even, given that it is greater than 3, is \( \frac{4}{7} \).