The probability that a student will pass the final examination in both English and Hindi 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 Hindi examination?
Solution and Explanation
Let A and B be the events of passing English and Hindi examinations respectively.
Accordingly, P (A and B) = 0.5, P (not A and not B) = 0.1, i.e.(A'∩B') =0.1
P(A) = 0.75
Now (AUB)'=(A'∩B') [De Morgans Law]
∴P(AUB)'=P(A'∩B') =0.1
P(AUB)=1-P(AUB)'=1-0.1=0.9
We know that P (A or B) = P(A) + P(B) - P (A and B)
∴0.9 = 0.75 + P(B) - 0.5
\(⇒ P(B) = 0.9 - 0.75 + 0.5\)
\(⇒ P(B) = 0.65 \)
Thus, the probability of passing the Hindi examination is 0.65.
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Concepts Used:
Axiomatic Approach to Probability
The axiomatic probability perspective is a unifying perspective in which the coherent conditions used in theoretical and experimental probability exhibit subjective probability. Kolmogorov's set of rules or axioms is put to all types of probability. They are known as Kolmogorov's 3 axioms by mathematicians. You can use axiomatic probability to calculate the likelihood of an event that is occurring or not occurring.
The 3 axioms are applicable to all other probability perspectives. This viewpoint is defined as the probability of any function from numbers to events that are satisfied by the three axioms listed below:
- The greatest possible probability is one, and the least possible probability is zero.
- A determined event has a probability of one.
- Two mutually exclusive events cannot happen at the same time, but the union of events states that any one of them can.
