MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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**Probability with a Deck of Cards**

When you draw two cards from a standard deck of 52 cards, and once the first card is drawn, it is not put back, you can determine specific probabilities as follows:

a.) What is the probability of drawing a red card on the first draw and a red card on the second draw?
b.) What is the probability of drawing a 7 on the first card and a King on the second card?

### Explanation with Solutions:

**a.) Probability of drawing a red card on the first draw and a red card on the second draw:**

1. There are 26 red cards in a deck of 52 cards.
2. Probability of drawing a red card first: \( P(\text{Red on first draw}) = \frac{26}{52} = \frac{1}{2} \)
3. After drawing the first red card, 25 red cards remain out of 51 total cards.
4. Probability of drawing another red card: \( P(\text{Red on second draw | Red on first draw}) = \frac{25}{51} \)
5. Therefore, the combined probability: 
   \[
   P(\text{Red on first and Red on second}) = P(\text{Red on first}) \times P(\text{Red on second | Red on first}) = \frac{1}{2} \times \frac{25}{51} = \frac{25}{102}
   \]

**b.) Probability of drawing a 7 on the first card and a King on the second card:**

1. There are 4 sevens in a deck of 52 cards.
2. Probability of drawing a seven first: \( P(7 \text{ on first draw}) = \frac{4}{52} = \frac{1}{13} \)
3. After drawing the seven, we have 4 Kings remaining out of 51 total cards.
4. Probability of drawing a King: \( P(\text{King on second draw | 7 on first draw}) = \frac{4}{51} \)
5. Therefore, the combined probability:
   \[
   P(7 \text{ on first and King on second}) = P(7 \text{ on first}) \times P(\text{King on second | 7 on first}) = \frac{1}{13} \times \frac{4}{51
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Transcribed Image Text:**Probability with a Deck of Cards** When you draw two cards from a standard deck of 52 cards, and once the first card is drawn, it is not put back, you can determine specific probabilities as follows: a.) What is the probability of drawing a red card on the first draw and a red card on the second draw? b.) What is the probability of drawing a 7 on the first card and a King on the second card? ### Explanation with Solutions: **a.) Probability of drawing a red card on the first draw and a red card on the second draw:** 1. There are 26 red cards in a deck of 52 cards. 2. Probability of drawing a red card first: \( P(\text{Red on first draw}) = \frac{26}{52} = \frac{1}{2} \) 3. After drawing the first red card, 25 red cards remain out of 51 total cards. 4. Probability of drawing another red card: \( P(\text{Red on second draw | Red on first draw}) = \frac{25}{51} \) 5. Therefore, the combined probability: \[ P(\text{Red on first and Red on second}) = P(\text{Red on first}) \times P(\text{Red on second | Red on first}) = \frac{1}{2} \times \frac{25}{51} = \frac{25}{102} \] **b.) Probability of drawing a 7 on the first card and a King on the second card:** 1. There are 4 sevens in a deck of 52 cards. 2. Probability of drawing a seven first: \( P(7 \text{ on first draw}) = \frac{4}{52} = \frac{1}{13} \) 3. After drawing the seven, we have 4 Kings remaining out of 51 total cards. 4. Probability of drawing a King: \( P(\text{King on second draw | 7 on first draw}) = \frac{4}{51} \) 5. Therefore, the combined probability: \[ P(7 \text{ on first and King on second}) = P(7 \text{ on first}) \times P(\text{King on second | 7 on first}) = \frac{1}{13} \times \frac{4}{51
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