Applied Mathematics

Probability Distribution

Medium

applied

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:

X	0	1	2
P(X)	7/15	7/15	1/15

X	0	1	2
P(X)	3/8	3/8	1/4

X	0	1	2
P(X)	1/4	1/2	1/4

X	0	1	2
P(X)	3/28	15/28	5/14

✅ Correct Option: 1

Sampling without replacement from 3 defective and 7 good clocks, with $\binom{10}{2}=45$ : $P(0)=\frac{\binom72}{45}=\frac{21}{45}=\frac{7}{15}$ , $P(1)=\frac{3\times7}{45}=\frac{7}{15}$ , $P(2)=\frac{3}{45}=\frac{1}{15}$ .

2026: 29 May Shift 1

The mean of the number of tails in three tosses of a coin is :

2022: 25 May Shift 1

If the probability distribution of a random variable X is given as

$x_i$	0	1	2	3
$p_i$	$2k^2$	$k^2$	$3k^2$	$k$

Then the mean of X is

2026: 21 May Shift 2

In a single throw of a die, if X denotes the number on its upper face, then the mean of X 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 :

2026: 30 May Shift 2

There are 10% defective pens. In a sample of randomly selected 10 pens, the probability that atmost one pen is defective, is

2026: 19 May Shift 2

A car hire firm has two cars, which is hire out day by day. The number of demands for cars on each day is distributed as a Poisson distribution with mean 1.5. Then which of the following is/are TRUE? (use $e^{-1.5} = 0.2231$ )

A. The probability of days when no car is required is 0.2231

B. The probability of days when some demand is refused is 0.1913

C. The probability of days when no car is required is 0.1913

D. The probability of days when some demand is refused is 0.2231

Choose the correct answer from the options given below:

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:

Solution

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