Question

Let e and f be two events of an experiment with sample space s. Suppose that pr(e) = 0.7 and pr(e' ∩ f') = 0.1 and pr(e ∩ f) = 0.2. What is the value of pr(f')?

Answer 1

The correct value of pr(f'), given the provided probabilities of other events and their intersections, is calculated using the Addition Rule of Probability and is found to be 0.6.

Step-by-step explanation:

The student is asking how to find the probability of the complement of an event, given information about certain events and their intersections. Specifically, they need to find the value of pr(f'), where pr(e) = 0.7, pr(e' ∩ f') = 0.1, and pr(e ∩ f) = 0.2.

To solve this, we can use the Addition Rule of Probability, which states that pr(e ∩ f) + pr(e' ∩ f') = pr(e) + pr(f') - pr(e ∩ f).
From this, we can deduce that pr(f') = pr(e ∩ f) + pr(e' ∩ f') - pr(e). Plugging in the given values:

• pr(f') = 0.2 + 0.1 - 0.7
• pr(f') = 0.3 - 0.7
• pr(f') = -0.4

This value for pr(f') cannot be correct since a probability cannot be negative. It seems we have made a mistake.

Let's correct it:

• pr(e ∩ f') + pr(e ∩ f) = pr(e)
• pr(e ∩ f') = pr(e) - pr(e ∩ f)
• pr(e ∩ f') = 0.7 - 0.2
• pr(e ∩ f') = 0.5

Because pr(e ∩ f') and pr(e' ∩ f') are complementary, we can add them to get pr(f').

• pr(f') = pr(e ∩ f') + pr(e' ∩ f')
• pr(f') = 0.5 + 0.1
• pr(f') = 0.6

Therefore, the correct value of pr(f') is 0.6.