Probability Test

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Probability Test - 58

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Question 1
1 / -0

A group of boys and girls know either English or Hindi. The number of boys and girls are in the ratio 1:4 given 30% of girls know Hindi and the rest of them know English. On other hand, 50% of the boys know Hindi and the rest of them know English. A student chosen at random from the group of student knows Hindi, the probability that the chosen student was a girl is

A
$$\frac{{12}}{{17}}$$

B
$$\frac{5}{{17}}$$

C
$$\frac{{12}}{{50}}$$

D
$$\frac{1}{{10}}$$

Solution
Question 2
1 / -0

If the range of a random variable $$X$$ is $${0,\ 1,\ 2,\ 3,....}$$ with $$P{X=K}=\dfrac {(k+1)a}{3^{k}}$$ for $$k\ge 0$$, then $$a=$$

A
$$2/3$$

B
$$4/9$$

C
$$89/27$$

D
$$16/81$$

Solution
Question 3
1 / -0

There are 5 students S1,S2,S3,S4,S5 in a music class and for them there are 5 seats in a row. On examination day, all five students are randomly allotted the five seats. Let Ti denote the event that Si and Si+1 do NOT sit adjacent to each other on examination day. (i=1,2,3,4) What is the probability that T1,T2,T3,T4,T5 all occur simultaneously on examination day? If the probability is of the form A/B, find A+B

A
25

B
47

C
52

D
67
Question 4
1 / -0

A dice is thrown twice and the sum of the numbers appearing is observed to be $$6$$ . What is the conditional probability that the number $$4$$ has appeared at least once?

A
$$2/ 3$$

B
$$2/ 5$$

C
$$1/ 5$$

D
None

Solution
Question 5
1 / -0

The c.d.f of a discrete r.v X isThen $$P\left(X=-3|X<0\right)$$

A
$$0.3333$$

B
$$0.35$$

C
$$0.55$$

D
$$0.25$$

Solution
Question 6
1 / -0

Lot A consist of 3G and 2D articles. Lot B consists of 4G and 1D article, A new lot C is formed by taking 3 articles from A and 2 from B. The probability that an article chosen at random from C is defective, is

A
$$\frac{1}{3}$$

B
$$\frac{2}{5}$$

C
$$\frac{8}{25}$$

D
none

Solution
Question 7
1 / -0

Two coins are tossed 1000 times and the outcomes are recorded as below:
Number of heads 2 1 0
Frequency 200 550 250
Based on this information, the probability for atmost one head is

A
$$\frac{1}{5}$$

B
$$\frac{1}{4}$$

C
$$\frac{4}{5}$$

D
$$\frac{3}{4}$$

Solution
Question 8
1 / -0

There are eight machines and it is known that exactly three of them are faulty. They are tested, one-by-one, in a random order till all the faulty machines are identified. Then the probability that only three tests are needed is

A
1/56

B
1/6

C
1/36

D
none of these

Solution
Question 9
1 / -0

A sample of 4 items is drawn at random with replacement from a lot of 10 items containing 3 defective items. If $$ X $$ denotes the number of defective items in the sample, then $$ P(0<X<3)= $$

A
$$ \frac{3}{10} $$

B
$$ \frac{4}{5} $$

C
$$ \frac{1}{2} $$

D
none of these

Solution
Question 10
1 / -0

A sample of 4 items is drawn at random with replacement from a lot of 10 items containing3 defective items. If $$X$$ denotes the number of defective items in the sample, then $$P ( 0 < X < 3 ) =$$

A
$$\frac { 3 } { 10 }$$

B
$$\frac { 4 } { 5 }$$

C
$$\frac { 1 } { 2 }$$

D
None of these

Solution