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NDA 2025
Exam
NDA
Year
2025
Subject
Mathematics
Chapter
Probability

NDA 2025 · Mathematics · Probability

The probability that a student passes Physics test is 2/3 and the...

The probability that a student passes Physics test is 2/32/3 and the probability that he passes both Physics test and English test is 11/1511/15. The probability that he passes at least one test is 4/54/5. What is the probability that he passes English test?

Options

  1. A11/1511/15
  2. B13/1513/15
  3. C14/1514/15
  4. D11

Correct answer

B. 13/1513/15

Step-by-step solution

Let PP be the event of passing the Physics test and EE be the event of passing the English test.

Given:
P(P)=23P(P) = \dfrac{2}{3}
P(P∩E)=1115P(P \cap E) = \dfrac{11}{15}
P(P∪E)=45P(P \cup E) = \dfrac{4}{5}

Using the addition theorem of probability:
P(P∪E)=P(P)+P(E)−P(P∩E)P(P \cup E) = P(P) + P(E) - P(P \cap E)

Substituting the given values:
45=23+P(E)−1115\dfrac{4}{5} = \dfrac{2}{3} + P(E) - \dfrac{11}{15}

P(E)=45−23+1115P(E) = \dfrac{4}{5} - \dfrac{2}{3} + \dfrac{11}{15}

Taking the LCM of the denominators, which is 1515:
P(E)=12−10+1115P(E) = \dfrac{12 - 10 + 11}{15}

P(E)=1315P(E) = \dfrac{13}{15}

Answer: 13/1513/15
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