What is the probability of drawing a black card or an Ace from a standard deck of cards?
What is the probability of drawing a black card or an Ace from a standard deck of cards?
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
![**Probability Question**
What is the probability of drawing a black card or an Ace from a standard deck of cards?
**Select one:**
[Options not provided]
---
To solve this probability question, consider the following:
- A standard deck of cards has 52 cards.
- There are two black suits: spades and clubs, each containing 13 cards.
- Total black cards = 13 (spades) + 13 (clubs) = 26 black cards.
- There are 4 Aces in total: Ace of spades, Ace of clubs, Ace of hearts, and Ace of diamonds.
- Of these, 2 Aces are black (spades and clubs).
- Use the formula for the probability of either/or events:
\[
P(\text{Black or Ace}) = P(\text{Black}) + P(\text{Ace}) - P(\text{Black and Ace})
\]
- Calculate the probabilities:
- \( P(\text{Black}) = \frac{26}{52} \)
- \( P(\text{Ace}) = \frac{4}{52} \)
- \( P(\text{Black and Ace}) = \frac{2}{52} \) (since there are 2 black Aces)
- Substitute into the formula:
\[
P(\text{Black or Ace}) = \frac{26}{52} + \frac{4}{52} - \frac{2}{52}
\]
- Simplify to find the probability.
This type of probability question helps students understand and apply basic probability rules, such as the addition rule for non-mutually exclusive events.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F29c548e8-67ee-420f-9864-c921ec696bc8%2F9fe44160-5d1b-44a4-b514-56ccbccda699%2Fptolpk_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Probability Question**
What is the probability of drawing a black card or an Ace from a standard deck of cards?
**Select one:**
[Options not provided]
---
To solve this probability question, consider the following:
- A standard deck of cards has 52 cards.
- There are two black suits: spades and clubs, each containing 13 cards.
- Total black cards = 13 (spades) + 13 (clubs) = 26 black cards.
- There are 4 Aces in total: Ace of spades, Ace of clubs, Ace of hearts, and Ace of diamonds.
- Of these, 2 Aces are black (spades and clubs).
- Use the formula for the probability of either/or events:
\[
P(\text{Black or Ace}) = P(\text{Black}) + P(\text{Ace}) - P(\text{Black and Ace})
\]
- Calculate the probabilities:
- \( P(\text{Black}) = \frac{26}{52} \)
- \( P(\text{Ace}) = \frac{4}{52} \)
- \( P(\text{Black and Ace}) = \frac{2}{52} \) (since there are 2 black Aces)
- Substitute into the formula:
\[
P(\text{Black or Ace}) = \frac{26}{52} + \frac{4}{52} - \frac{2}{52}
\]
- Simplify to find the probability.
This type of probability question helps students understand and apply basic probability rules, such as the addition rule for non-mutually exclusive events.
Expert Solution
Step 1
We know that
There are 52 cards in the deck divided into two colour i.e red(26) and black (26). These black cards divided into spade(13) and club (13) and red cards divided into heart(13) and diamond(13). These 13 are further divided into K, Q, J, 10, 9, 8, 7, 6, 5, 4, 3, 2, A. There are 12 face cards, 3 each of suit (Spade,club, heart, diamond) have K,Q,J.
Step by step
Solved in 2 steps
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