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:

9b less than 5 given that the first one is a 15?
give your answer in its simplest form.
p(second is less than 5|first is a 15) = 4/19
9c a number divisible by 5 given that the first card is a 15.
give your answer in its simplest form.
p(second is divisible by 5|first is a 15) = enter your next step here

Explanation:

Step1: Determine total remaining cards

After drawing 15 (1 card), remaining cards: \(20 - 1 = 19\)

Step2: Find numbers divisible by 5 initially

Numbers 1 - 20 divisible by 5: 5, 10, 15, 20 (4 numbers). But 15 is already drawn, so remaining: \(4 - 1 = 3\)

Step3: Calculate probability

Probability = \(\frac{\text{Remaining favorable}}{\text{Total remaining}} = \frac{3}{19}\)

Answer:

\(\frac{3}{19}\)