Question

1. from a set of 10 cards numbered 1 to 10, two cards are drawn at random without replacement. what is the probability that: 3a both numbers are even? probability = enter your next step here

Explanation:

Step1: Find number of even cards

Numbers 1 - 10: even numbers are 2,4,6,8,10. So 5 even cards.

Step2: Calculate total ways to draw 2 cards

Using combination formula \( C(n,r)=\frac{n!}{r!(n - r)!} \), total ways to draw 2 from 10: \( C(10,2)=\frac{10!}{2!8!}=\frac{10\times9}{2\times1}=45 \)

Step3: Calculate ways to draw 2 even cards

Ways to draw 2 from 5 even cards: \( C(5,2)=\frac{5!}{2!3!}=\frac{5\times4}{2\times1}=10 \)

Step4: Find probability

Probability = \( \frac{\text{Ways to draw 2 even}}{\text{Total ways to draw 2}}=\frac{10}{45}=\frac{2}{9} \)

Answer:

\(\frac{2}{9}\)