You draw two cards from a standard deck of 52 cards, once the first card is drawn it is not put back a.) Find P(red on the first draw and red on the second draw) = b.) Find P(7 on the first card and a King on the second card)=
You draw two cards from a standard deck of 52 cards, once the first card is drawn it is not put back a.) Find P(red on the first draw and red on the second draw) = b.) Find P(7 on the first card and a King on the second card)=
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F95e5613b-1a25-4b20-8027-b25d1244d9dc%2Fafebc89b-df97-4b92-921e-34aae82bd645%2Fg8dmmat_processed.jpeg&w=3840&q=75)
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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