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Probability Axioms and Conditional Probability Questions and Answers

11.

If a person who does not know typing is asked to type the manuscript of a book, the probability of the event that he will type it correctly without any mistake is ....

Exam Year(s)

MH SET - 2025, SET Exam - 2025,

Answer: B

The probability is 0.

The question describes an impossible event. A person who cannot type at all has no realistic chance of typing a whole book's manuscript without a single mistake, so the event is treated as impossible, and the probability of an impossible event is 0.

A probability of 1 is for a certain event, the opposite case. Fractions such as 3/4 and 2/3 would mean the person usually succeeds, which contradicts the premise that he does not know typing. The question is a standard illustration that probability ranges from 0 (impossible) to 1 (certain).

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12.

How many people must there be in a room before there is a 50% chance that two of them were born on the same day of the year ?

Exam Year(s)

UGC NET - 2013,

Answer: A

At least 23 people are needed for a better than 50% chance that two of them share a birthday, the birthday paradox. The probability that all of n people have different birthdays is \(\frac{365 \times 364 \times \cdots \times (365-n+1)}{365^{n}}\), which drops below 0.5 at n = 23.

The number 183 is about half of 365 and is the answer to a different question, how many people are needed for a 50% chance that one of them shares your own birthday. The numbers 366 and 730 relate to the pigeonhole principle, which guarantees a match but not at the 50% level.

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