Question
upstudy study bank question image url

10. A 6 -sided die is blased in such a way that the probability of a "six" appearing on top is \( 20 \% \) and all other possibilities have an equal chance of appearing on top. If the die is thrown 5 times, what is the probability that a "six" will appear at most 3 times? 0.0026 0.0080

Ask by Bryant Hart. in the United Arab Emirates
Mar 14,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

The probability that a "six" appears at most 3 times in 5 throws is approximately 0.9933.

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

Bonus Knowledge

To find the probability of rolling a "six" at most 3 times when throwing a biased die 5 times, we can use the binomial probability formula. Given that the probability of rolling a six \( p = 0.20 \) and the number of trials \( n = 5 \), we can calculate the probabilities for getting 0, 1, 2, and 3 sixes and sum them up. For each \( k \) (number of sixes), the probability is calculated as: \[ P(X = k) = \binom{n}{k} p^k (1-p)^{n-k} \] Calculating for \( k = 0, 1, 2, 3 \): 1. For \( k = 0 \): \[ P(X=0) = \binom{5}{0} (0.20)^0 (0.80)^5 \approx 0.32768 \] 2. For \( k = 1 \): \[ P(X=1) = \binom{5}{1} (0.20)^1 (0.80)^4 \approx 0.40960 \] 3. For \( k = 2 \): \[ P(X=2) = \binom{5}{2} (0.20)^2 (0.80)^3 \approx 0.20480 \] 4. For \( k = 3 \): \[ P(X=3) = \binom{5}{3} (0.20)^3 (0.80)^2 \approx 0.05120 \] Now, summing all the probabilities: \[ P(X \leq 3) = P(X=0) + P(X=1) + P(X=2) + P(X=3) \approx 0.32768 + 0.40960 + 0.20480 + 0.05120 \approx 0.99328 \] Thus, the probability that a "six" will appear at most 3 times in 5 rolls of this die is approximately \( 0.9933 \). So the answer to the problem is neither of the options provided (0.0026 or 0.0080). 0.9933

Related Questions

Latest Probability Questions

Try Premium now!
Try Premium and ask Thoth AI unlimited math questions now!
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