In a discount store, 12% of the 100 cups in stock have some unnoticeable defect. What is the probability of buying 12 cups that don’t have any defect? And what is the probability of getting all 12 cups having a defect?
The correct answer and explanation is:
Explanation:
In a discount store, 12% of the 100 cups in stock have some unnoticeable defect, meaning that the probability of selecting a defective cup is 0.12, while the probability of selecting a non-defective cup is 0.88.
We need to determine:
- The probability of purchasing 12 cups that are all non-defective.
- The probability of purchasing 12 cups that are all defective.
1. Probability of Selecting 12 Non-Defective Cups
Since each cup is chosen independently, the probability of picking 12 non-defective cups is given by: P(all non-defective)=(0.88)12P(\text{all non-defective}) = (0.88)^{12}
Using calculations, this probability is approximately 0.216 (21.57%).
2. Probability of Selecting 12 Defective Cups
Similarly, the probability of picking 12 defective cups is: P(all defective)=(0.12)12P(\text{all defective}) = (0.12)^{12}
This probability is extremely small, approximately 8.92×10−128.92 \times 10^{-12} (almost zero).
Interpretation:
- There is a 21.57% chance that all 12 cups selected are non-defective, meaning it is quite likely.
- The chance of all 12 cups being defective is almost zero, meaning it is practically impossible.
Now, I’ll generate an image illustrating the probability distribution.
The bar chart above illustrates the probability distribution of selecting different numbers of non-defective cups when purchasing 12 cups. The red bar highlights the probability of selecting all 12 cups as non-defective, which is approximately 21.57%. The probability of selecting all 12 defective cups is so small that it is practically negligible.