Learning starts with a question. Asking is a signal for knowledge request!
First time here? Checkout the FAQs!

How "image search" works

1 like 0 dislike
Two cards are drawn at random from an ordinary deck of 52 playing cards. What is the probability of getting two aces if

(a) the first card is replaced before the second card is drawn;
(b) the first card is not replaced before the second card is drawn?
in Data Science & Statistics by Diamond (55.6k points) | 468 views

1 Answer

0 like 0 dislike
Best answer
(a) Since there are four aces among the 52 cards, we get
\frac{4}{52} \cdot \frac{4}{52}=\frac{1}{169}

(b) Since there are only three aces among the 51 cards that remain after one ace has been removed from the deck, we get
\frac{4}{52} \cdot \frac{3}{51}=\frac{1}{221}
Note that
\frac{1}{221} \neq \frac{4}{52} \cdot \frac{4}{52}
so independence is violated when the sampling is without replacement.
by Diamond (55.6k points)

Related questions

1 like 0 dislike
1 answer
2 like 0 dislike
1 answer

Join MathsGee Q&A, where you get instant answers to your questions from our AI, AstraNova and verified by human experts. We use a combination of generative AI and human experts to provide you the best solutions to your problems.

On the MathsGee Q&A, you can:

1. Get instant answer to your questions

2. Convert image to latex

3. AI-generated answers and insights

4. Get expert-verified answers

5. Vote on questions and answers

6. Tip your favorite community members

7. Join expert live video sessions (Paid/Free)

8. Earn points by participating

9. Take a course

10. Enjoy our interactive learning resources

Posting on the MathsGee Q&A

1. Remember the human

2. Act like you would in real life

3. Find original source of content

4. Check for duplicates before publishing

5. Read the community guidelines

MathsGee Q&A Rules

1. Answers to questions will be posted immediately after moderation

2. Questions will be queued for posting immediately after moderation

3. Depending on the number of messages we receive, you could wait up to 24 hours for your message to appear. But be patient as posts will appear after passing our moderation.

MathsGee Q&A

MathsGee Q&A