Financial Risk Manager Part 1

These events are not independent. If the first card is the king of hearts then there is one less red card in the deck so the chance of getting a red is now (25/51 = 49.02%).

Detailed Explanation:

1. Initial deck composition: A standard 52-card deck has 26 red cards (13 hearts + 13 diamonds) and 26 black cards (13 spades + 13 clubs).

2. Condition given: The first card drawn is the King of Hearts, which is a red card.

3. After drawing the first card:

   • Total cards remaining: 51
   • Red cards remaining: 25 (since one red card, the King of Hearts, has been removed)
   • Black cards remaining: 26 (unchanged)

4. Probability calculation:

   • Probability that the second card is red = (Number of red cards remaining) / (Total cards remaining)
   • P(2nd card is red | 1st card is King of Hearts) = 25/51
   • 25/51 ≈ 0.4902 = 49.02%

5. Why not 50%: The events are not independent because drawing the King of Hearts changes the composition of the deck. If the events were independent, the probability would be 26/52 = 50%, but conditional probability accounts for the change in sample space.

6. Why not other options:

   • 51%: No mathematical basis for this value
   • 50%: Would be correct if events were independent or if sampling with replacement
   • 1%: Far too low, represents misunderstanding of probability