Question

Given: p(e) = 0.44, p(f) = 0.47, and p(e ⋃ f) = 0.71, find p(e ⋂ f) .

a) 0.15
b) 0.26
c) 0.30
d) 0.53

Answer 1

To calculate the probability of events e and f both occurring, p(e ⋂ f), use the formula p(e ⋂ f) = p(e) + p(f) - p(e ⋅ f). Based on the given probabilities, p(e ⋂ f) equals 0.20, which is not one of the provided options.

Step-by-step explanation:

To find p(e ⋂ f), which is the probability of both events e and f occurring, we can use the principle that p(e ⋂ f) = p(e) + p(f) - p(e ⋅ f). We were given that p(e) = 0.44, p(f) = 0.47, and p(e ⋅ f) = 0.71.

Let's use the given values to calculate p(e ⋂ f):

p(e ⋂ f) = p(e) + p(f) - p(e ⋅ f)
= 0.44 + 0.47 - 0.71
= 0.91 - 0.71
= 0.20

So, the correct answer is none of the options given, as the calculation yields 0.20, which does not match any options a-d.