Question

1. two cards are randomly drawn without replacement from a deck of cards numbered from 1 to 20. what is the probability that the second card is:

9a an even number given that the first card is a 2?
give your answer in its simplest form.
$p(\text{second card is even}|\text{first card is a 2}) = $

Explanation:

Step1: Determine remaining cards and even numbers

After drawing 2 (an even number) first, there are \(20 - 1=19\) cards left. Initially, there are 10 even numbers (2,4,6,8,10,12,14,16,18,20). After removing 2, there are \(10 - 1 = 9\) even numbers left.

Step2: Calculate conditional probability

The conditional probability \(P(\text{second card is even}|\text{first card is a } 2)\) is the number of remaining even numbers divided by the number of remaining cards. So it is \(\frac{9}{19}\).

Answer:

\(\frac{9}{19}\)