Tamil Nadu Board of Secondary EducationSSLC (English Medium) Class 10th

The probability that a student will pass the final examination in both English and Tamil is 0.5 and the probability of passing neither is 0.1. If the probability of passing the English examination i - Mathematics

Sum

The probability that a student will pass the final examination in both English and Tamil is 0.5 and the probability of passing neither is 0.1. If the probability of passing the English examination is 0.75, what is the probability of passing the Tamil examination?

Solution

Let A be the event of getting student pass in English

Let B be the event of getting student pass in Tamil

P(A ∩ B) = 0.5 = 1/2

P(A) = 0.75 = 75/100 = 3/4

P(A ∪ B) = 0.1

P(A ∪ B) = 1/10

1 − P(A ∪ B) = 1/10

P(A ∪ B) = 1 - 1/10

P(A ∪ B) = 9/10

P(A) + P(B) − P(A ∩ B) = 9/10

= 3/4 + "P"("B") - 1/2 = 9/10

P(B) = 9/10 + 1/2 - 3/4

= (18 + 10 - 15)/20

= 13/20

Probability of passing the tamil examination is 13/20

Concept: Algebra of Events
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