Algebra

Probability

Easy

common

In a box containing 100 bulbs, 10 are defective. Then the probability, that out of a sample of 5 bulbs none is defective, is:

$10^{-1}$

$\left(\frac{1}{2}\right)^5$

$\left(\frac{9}{10}\right)^5$

$\left(\frac{9}{10}\right)$

✅ Correct Option: 3

Probability that one bulb is non-defective $= \frac{90}{100} = \frac{9}{10}$ . Treating selections as independent (binomial model), probability all 5 are non-defective $= \left(\frac{9}{10}\right)^5$ .

2025: 13 May Shift 2

The probability of not getting 53 Sundays in a leap year is

2025: 30 May Shift 1

A random variable y has the following probability distribution

y	1	2	3	4	5
P(y)	2k	3k	k	4k	5k

Match List-I with List-II

List-I	List-II
(A) $P(y > 2)$	(I) $2/5$
(B) k	(II) $2/3$
(C) $P(y \leq 3)$	(III) $8/15$
(D) $P(2 \leq y \leq 4)$	(IV) $1/15$

Choose the correct answer from the options given below:

2025: 22 May Shift 1

Five dice are thrown simultaneously. If the occurrence of an even number in a single dice is considered a success, then the probability of at most 3 successes 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

2025: 30 May Shift 1

Match List-I with List-II

Let $A$ and $B$ be two events such that $P(A) = 0.2$ , $P(B) = 0.4$ , $P(B|A) = 0.5$

List-I	List-II
(A) $P(A \cap B)$	(I) $0.5$
(B) $P(A\vert B)$	(II) $0.8$
(C) $P(A \cup B)$	(III) $0.25$
(D) $P(A')$	(IV) $0.1$

Choose the correct answer from the options given below:

In a box containing 100 bulbs, 10 are defective. Then the probability, that out of a sample of 5 bulbs none is defective, is:

Solution

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