Kept getting the wrong answer? binomial conditional probability

Click For Summary
SUMMARY

The discussion revolves around calculating the probability of a coffee connoisseur correctly identifying coffee types under the assumption of random guessing. The user initially calculated the probability using the binomial formula C(5,4) * 0.75^4 * 0.25 for exactly 4 correct answers and added 0.75^5 for exactly 5 correct answers, resulting in 0.6328. However, the correct approach involves recognizing that if she is guessing, the probability of success for each cup is 0.5, leading to a different calculation method.

PREREQUISITES
  • Understanding of binomial probability distribution
  • Familiarity with combinatorial mathematics (C(n, k))
  • Knowledge of conditional probability concepts
  • Basic statistical analysis skills
NEXT STEPS
  • Study the binomial probability formula and its applications
  • Learn about conditional probability and its implications in real-world scenarios
  • Explore combinatorial mathematics, specifically combinations and permutations
  • Practice problems involving probability distributions and statistical inference
USEFUL FOR

Students in statistics, data analysts, and anyone interested in understanding probability theory and its applications in real-life scenarios.

mtingt
Messages
13
Reaction score
0
Product Testing A supposed coffee connoisseur claims she can distinguish between a cup of instant coffee and a cup of drip coffee 75% of the time. You give her 5 cups of coffee and tell her that you will grant her claim if she correctly identifies at least 4 of the 5 cups.

(a) What are her chances of having her claim granted if she is in fact only guessing?

i did
C(5,4)* .75^4 *.25 get the exactly 4 add .75^5 to get exactly 5.
i got 0.6328 but my online homework kept saying that it 's wrong.
 
Physics news on Phys.org
Hint: consider what would be the probability of success if she was testing a single cup and only guessing.

Edit: this thread belongs in the homework forums
 

Similar threads

Conditional Probability + Poisson Distribution
  • · Replies 14 ·
Replies
14
Views
3K
Roll 5 Dice Simultaneously: Probabilities and Conditional Probability
  • · Replies 11 ·
Replies
11
Views
3K
S1 Probability - Binomial & Geometric Distribution
  • · Replies 7 ·
Replies
7
Views
3K
Probability of getting an ace in case of a loaded die
  • · Replies 11 ·
Replies
11
Views
3K
Conditional probability exercise
  • · Replies 2 ·
Replies
2
Views
3K
Binomial probability, similar to lottery problems.
  • · Replies 1 ·
Replies
1
Views
3K
Why Does Calculating Binomial Probabilities Differ from Simple Outcome Ratios?
  • · Replies 1 ·
Replies
1
Views
2K
High School Probability in a dice game
  • · Replies 41 ·
2
Replies
41
Views
6K
Short Title:Probability Homework Questions
  • · Replies 4 ·
Replies
4
Views
3K
High School Conditional Probability, Independence, and Dependence
  • · Replies 10 ·
Replies
10
Views
3K