Applied Mathematics

Probability Distribution

Medium

applied

Ajay is a vendor who informs that there are 2% rotten apples in the fruit bag. Find the probability that a sample of 10 apples will include not more than one rotten apple.

$\left(\dfrac{98}{100}\right)^{10}\left(\dfrac{1}{5}\right)$

$\left(\dfrac{98}{100}\right)^9\left(\dfrac{59}{50}\right)$

$\left(\dfrac{98}{100}\right)^9(5)$

$\left(\dfrac{98}{100}\right)^9\left(\dfrac{59}{100}\right)$

✅ Correct Option: 2

Binomial with $n=10$ , $p=0.02$ . $P(X\le1)=(0.98)^{10}+10(0.02)(0.98)^9=(0.98)^9(0.98+0.2)=\left(\dfrac{98}{100}\right)^9\left(\dfrac{59}{50}\right)$ .

2023: 11 Aug Shift 1

The probability distribution of a discrete random variable X is given by :

X	30	10	-10
P(X)	1/5	3/10	1/2

then E(X) is equals to

2023: 23 May Shift 3

If the mean of a binomial distribution is 12 and its standard deviation is 2, then the number of trials is :

2023: 15 June Shift 2

Match List - I with List - II.

List - I	List - II
(A) In a binomial distribution, if $n = 10$ , $q = 0.25$ , then its mean is	(I) 12
(B) If the mean of a binomial distribution is 6 and its variance is 3, then p is	(II) 7.5
(C) In a binomial distribution, the probability of getting a success is $\frac{1}{4}$ and the standard distribution is 3, then its mean is	(III) 16
(D) If the mean and variance of a binomial distribution are 4 and 3 respectively, then the number of trials is	(IV) $\frac{1}{2}$

Choose the correct answer from the options given below :

2026: 30 May Shift 2

Match List-I with List-II

List-I	List-II
(A) Mean of a normal variate X is 12 and standard deviation is 4, then the Z-score of data point 20 is	(I) 1
(B) If X is Poisson variate such that P(X=1) = 2P(X=2), then the mean of X is	(II) 8
(C) In a binomial distribution, if mean is 5 and variance is 4, then the number of trials is	(III) 2
(D) In a binomial distribution, if n = 20 and q = 0.6, then its mean is	(IV) 25

Choose the correct answer from the options given below:

2026: 30 May Shift 1

A box containing 10 wall clocks has three defective pieces in it. If random sample of two clocks is taken from the box, then the probability distribution of defective clocks is:

2023: 23 May Shift 3

A shopkeeper wants to check the average number of cars sold per call. Past record of sales is shown below:

Sale of cars (Units)	0	1	2	3
Probabilities	$\frac{1}{6}$	$\frac{1}{2}$	$\frac{3}{10}$	$\frac{1}{30}$

The expected number of cars sold is :

Ajay is a vendor who informs that there are 2% rotten apples in the fruit bag. Find the probability that a sample of 10 apples will include not more than one rotten apple.

Solution

Related questions:

Keyboard Shortcuts

CUET Mathematics Past Year Questions (Topic-Wise)