If for two events A and B, Pr(A)= \frac{1}{5} , and Pr(B)= \frac{3}{5} , and Pr(A \cup B)= \frac{7}{10} , then Pr(A ∩ B) is equal to:

Question

If for two events A and B, Pr(A)= \frac{1}{5} , and Pr(B)= \frac{3}{5} , and Pr(A \cup B)= \frac{7}{10} , then Pr(A ∩ B) is equal to:

BlackTom AI · Accepted Answer

To find Pr(A ∩ B) we can use the inclusion–exclusion principle: Pr(A ∪ B) = Pr(A) + Pr(B) − Pr(A ∩ B).
Rearranging gives Pr(A ∩ B) = Pr(A) + Pr(B) − Pr(A ∪ B).
Plugging in the given values: Pr(A ∩ B) = (1/5) + (3/5) − (7/10).
Compute (1/5) + (3/5) = 4/5 = 8/10. Then 8/10 − 7/10 = 1/10.
Therefore, the intersection probability is 1/10. This matches the option listed as 'a. 1/10'.

Why this makes sense: the intersection cannot be larger than either Pr(A) or Pr(B), and the union cannot exceed 1. The calculated 1/10 sits within those bounds and is consistent with all provided marginals.

Why other hypothetical options (if present) would be wrong: if you tried to add Pr(A ∩ B) to Pr(A ∪ B) and compare to Pr(A) + Pr(B), you’d violate the inclusion–exclusion relationship. If you assumed independence without the given union, you’d compute Pr(A)Pr(B) = (1/5)(3/5) = 3/25 = 0.12, which is 0.12, not aligning with the provided union probability 7/10; hence independence is not implied by the data.

MUF0092 Mathematics Unit 2-SEM 1-2025 7.15 Probability and discrete probability distributions quiz

If for two events A and B, Pr(A)= \frac{1}{5} , and Pr(B)= \frac{3}{5} , and Pr(A \cup B)= \frac{7}{10} , then Pr(A ∩ B) is equal to:

View Explanation

Log in for full answers

Similar Questions

There are 52 balls in a box. 13 are red, 20 are white, and the other are blue. You pick up 5 balls without replacement. What is the probability that you pick up at least 1 red balls?

Question at position 11 If P(A) = 0.24 and P( B )=0.52 and A and B are independent, what is P(A or B)?0.12480.6352Approximately 00.760.28

Question at position 6 In a certain town, 20% of the households have an electric vehicle, 40% have a hybrid vehicle, and 10% have both. What percent of households have neither an electric nor a hybrid vehicle?0%30%10%70%50%

You have a trick coin that lands on Head 70% of the time. You flip this coin twice. What is the probability you have 1 head and 1 tail? Give the answer as a decimal ( .0.58 for a probability of 58%)

位置1的问题 Suppose X is a random variable representing rolling a six-sided dice. Assume the dice is fair, so there is an equal probability of rolling any number 1 through 6. What is the following probability? P(2≤X≤5) 13231256清除选择

位置1的问题 Suppose X is a random variable representing rolling a six-sided dice. Assume the dice is fair, so there is an equal probability of rolling any number 1 through 6. What is the following probability? P(2≤X≤5) 13562312清除选择

More Practical Tools for Students Powered by AI Study Helper

Homework AI Solver

Stylized AI Paper Writer

Plagiarism Checker Assistant

Citation AI Academic Writing Tool

In-Class Translation Assistant

AI Note Generator

AI Quiz Answers

Past Exam Questions from University Test Bank

Smart Practice Assistant

Adaptive Practice

Making Your Study Simpler