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}) = \frac{9}{19} \\) 9b less than 5 given that the first one is a 15? give your answer in its simplest form. \\( p(\text{second is less than 5}|\text{first is a 15}) = \\)

Explanation:

Step1: Determine remaining cards

After drawing 15, 19 cards remain (20 - 1 = 19).

Step2: Count favorable cards

Numbers less than 5: 1, 2, 3, 4 (4 numbers).

Step3: Calculate probability

Probability = favorable / total = $\frac{4}{19}$.

Answer:

$\frac{4}{19}$