Question

Given:

Probability of passing both English and Hindi: P(English and Hindi) = 0.5
Probability of passing neither: P(Neither) = 0.1
Probability of passing English: P(English) = 0.75
What is the probability of passing the Hindi examination?
(a) 0.45
(b) 0.65
(c) 0.75
(d) 0.9

Answer 1

The probability of passing the Hindi examination is 0.65 when calculated using the given probabilities of passing English, passing both, and passing neither.

Step-by-step explanation:

To find the probability of passing Hindi, we need to use the given probabilities. We know that the probability of passing both English and Hindi is P(English and Hindi) = 0.5, the probability of passing neither is P(Neither) = 0.1, and the probability of passing English is P(English) = 0.75. To find the probability of passing only Hindi, we can use the formula of the probability of the union of two events, which is P(A or B) = P(A) + P(B) - P(A and B).

In this case, P(English or Hindi) is equivalent to 1 - P(Neither), since either English or Hindi or both must be passed if not neither. Thus, P(English or Hindi) = 1 - 0.1 = 0.9.

Now substituting the values into the equation, we get:
0.9 = P(English) + P(Hindi) - P(English and Hindi), which simplifies to:
0.9 = 0.75 + P(Hindi) - 0.5. Solving for P(Hindi), we find that P(Hindi) = 0.9 - 0.75 + 0.5 = 0.65. Hence, the probability of passing the Hindi examination is 0.65.