Question
A husband and wife discover that there is a \( 4 \% \) probability of their passing on a hereditary disease to any of their
children. If they plan to have three

A husband and wife discover that there is a \( 4 \% \) probability of their passing on a hereditary disease to any of their children. If they plan to have three children, what is the probability of the event that at least one child will inherit the disease? The probability is \( \square \% \). (Round to one decimal place as needed.)

Ask by Blake Barnett.
Jan 23,2025 02:54

UpStudy AI Solution

Tutor-Verified Answer

Answer

The probability is \( 11.5\% \).

Solution

Sign in to Unlock Answers for Free!

A Learning Platform Trusted by Millions of Real Students and Teachers.

star-icon Unlock

Answered by UpStudy AI and reviewed by a Professional Tutor

Extra Insights

To find the probability that at least one child will inherit the hereditary disease, we can first find the probability that none of the children inherit the disease and then subtract that value from 1. The probability that a child does not inherit the disease is \( 1 - 0.04 = 0.96 \). If they have three children, the probability that none of them inherit the disease is: \[ P(\text{none inherit}) = (0.96)^3 = 0.96 \times 0.96 \times 0.96 \approx 0.884736. \] Now, the probability that at least one child inherits the disease is: \[ P(\text{at least one inherits}) = 1 - P(\text{none inherit}) \approx 1 - 0.884736 \approx 0.115264. \] To express this as a percentage, we multiply by 100: \[ P(\text{at least one inherits}) \approx 0.115264 \times 100 \approx 11.5\%. \] So, the probability is \( 11.5\% \).
Try Premium now!
Upgrade to Premium and explore the full power of UpStudy!
Maybe later Go Premium
Study can be a real struggle
Why not UpStudy it?
Select your plan below
Premium

You can enjoy

Start now
  • Step-by-step explanations
  • 24/7 expert live tutors
  • Unlimited number of questions
  • No interruptions
  • Full access to Answer and Solution
  • Full Access to PDF Chat, UpStudy Chat, Browsing Chat
Basic

Totally free but limited

  • Limited Solution
Welcome to UpStudy!
Please sign in to continue the Thoth AI Chat journey
Continue with Email
Or continue with
By clicking “Sign in”, you agree to our Terms of Use & Privacy Policy