Algebra

Probability

Easy

common

The mean of the number of heads in a simultaneous toss of three coins is :

$\frac{1}{2}$

$\frac{3}{2}$

✅ Correct Option: 3

Number of heads X follows binomial distribution with $n=3, p=\frac{1}{2}$ .

Mean $= np = 3 \times \frac{1}{2} = \frac{3}{2}$ .

2022: 23 Aug Shift 1

If an unbiased coin is tossed 10 times, probability of obtaining more head than tail is :

2025: 15 May Shift 1

Under which of the following conditions the Poisson distribution is the limiting case of, binomial distribution:

(A) The number of trials is indefinitely large.

(B) The probability of success for each trial is indefinitely small.

(D) The probability of success for each trial is indefinitely large.

Choose the correct answer from the options given below:

2025: 13 May Shift 2

A man is known to speak truth 3 out of 4 times. He throws a die and reports that it is four. The probability that it is actually four is

2026: 29 May Shift 2

If A, B and C are three independent events such that P(A)=P(B)=P(C)=x, then P(at least two of A, B, C occur) =

2025: 15 May Shift 2

If a random variable $X$ has the following probability distribution:

X	0	1	2	3	4
P(X)	k	2k	3k	k²	6k²

, then

Match List-I with List-II

Choose the correct answer from the options given below:

2025: 13 May Shift 1

Which of the following statements are correct?

(A) If E and F are independent events then $P(E \cap F) = P(E) \cdot P(F)$

(B) If E and F are mutually exclusive events, then $P(E \cup F) = P(E) + P(F) - P(E) \cdot P(F)$

(C) The conditional probability of an event E, given the occurrence of the event F is given by $\frac{P(E \cap F)}{P(F)}, P(F) \neq 0$

(D) If E and F be the events associated with the sample space S of an experiment, then $P(\overline{E}|F) = 2 - P(E|F)$

Choose the correct answer from the options given below:

Solution