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In an examination, 30% of students have failed in subject I, 20% of the students have failed in subject II and 10% have failed in both subject I and subject II. A student is selected at random - Mathematics and Statistics

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Sum

In an examination, 30% of students have failed in subject I, 20% of the students have failed in subject II and 10% have failed in both subject I and subject II. A student is selected at random, what is the probability that the student has failed in at least one subject?

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Solution

Let A be the event that the student failed in Subject I
B be the event that the student failed in Subject II

Then P(A) = 30% = `30/100`

P(B) = 20% = `20/100`

And P(A ∩ B) = 10% = `10/100 `

P (student failed in at least one subject)
= P(A ∪ B) = P(A) + P(B) – P(A∩ B)

= `30/100 + 20/100 - 10/100`

= `40/100`

= 0.40

Concept: Conditional Probability
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