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

Math Image Search excels with single, zoomed-in, well-cropped math images (jpg/png); avoid selfies/diagrams; view demos for Math Image Search Demo and Ask a Question Using Text/Image Demo.

2 like 0 dislike
If the independent probabilities that three people \(\mathrm{A}, \mathrm{B}\) and \(\mathrm{C}\) will be alive in 30 years time are \(0.4,0.3,0.2\) respectively, calculate the probability that in 30 years' time,

(a) all will be alive
(b) none will be alive
(c) only one will be alive
(d) at least one will be alive
in Data Science & Statistics by Diamond (50,375 points) | 248 views

1 Answer

0 like 0 dislike
Best answer
(a) \(P=P(A) \times P(B) \times P(C)=0.4 \times 0.3 \times 0.2=0.024\)
(b) We use the notation \(P(\bar{A})\) to mean "the probability that \(A\) will not occur". So:
&P=P(\bar{A}) \times P(\bar{B}) \times P(\bar{C}) \\
&=0.6 \times 0.7 \times 0.8 \\
(c) \(P=P(A\) only alive \()+P(B\) only alive \()+P(C\) only alive \()\)
&=[P(A) \times P(\bar{B}) \times P(\bar{C})]+[P(\bar{A}) \times P(B) \times P(\bar{C})]+[P(\bar{A}) \times P(\bar{B}) \times P(C)] \\
&=0.4 \times 0.7 \times 0.8+0.6 \times 0.3 \times 0.8+0.6 \times 0.7 \times 0.2 \\
&=0.452 \\
&\text { (d) } P=1-\{P(\bar{A}) \times P(\bar{B}) \times P(\bar{C})\}=1-0.336=0.664
by Diamond (50,375 points)

Related questions

Join MathsGee Questions & Answers, where you get instant answers to your questions from our AI, GaussTheBot 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 Questions & Answers, 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 Questions & Answers

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 Questions & Answers 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 Questions & Answers

MathsGee Questions & Answers

MathJax.Hub.Config({ tex2jax: { inlineMath: [ ['$','$'], ["\\(","\\)"] ], config: ["MMLorHTML.js"], jax: ["input/TeX"], processEscapes: true } }); MathJax.Hub.Config({ "HTML-CSS": { linebreaks: { automatic: true } } });