Question

Ten cards in a pack are numbered as 1, 2, 3, . . .10. The probability of drawing a card with an even number or a number which is a multiple of 5 from the pack is

• A. 4/10
• B. 6/10
• C. 2/10
• D. 3/10

Answer 1

The Correct Option is B

Step 1: List all possible outcomes. The total number of cards is \( 10 \), numbered as \( \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\} \). Step 2: Identify favorable outcomes. The event involves drawing a card that is: An even number: \( \{2, 4, 6, 8, 10\} \) A multiple of 5: \( \{5, 10\} \) The union of these two sets is \( \{2, 4, 5, 6, 8, 10\} \), as \( 10 \) is common to both sets. Step 3: Count the favorable outcomes. The number of favorable outcomes is: \[ |\text{Favorable outcomes}| = 6 \] Step 4: Calculate the probability. The probability is given by: \[ P(\text{Favorable outcome}) = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{6}{10} \]