Practice Probability Multiple Choice Questions Quiz-3 - MCQGeeks.com

Q.1

A box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that all the four bulbs are defective.

$$\frac{{62}}{{63}}$$
$$\frac{{125}}{{126}}$$
$$\frac{{1}}{{63}}$$
$$\frac{{1}}{{126}}$$

Q.2

Four dice are thrown simultaneously. Find the probability that all of them show the same face.

$$\frac{{1}}{{216}}$$
$$\frac{{1}}{{36}}$$
$$\frac{{4}}{{216}}$$
$$\frac{{3}}{{216}}$$

Q.3

A five-digit number is formed by using digits 1, 2, 3, 4 and 5 without repetition. What is the probability that the number is divisible by 4?

$$\frac{{1}}{{5}}$$
$$\frac{{5}}{{6}}$$
$$\frac{{4}}{{5}}$$
None of these

Q.4

An urn contains 6 red, 5 blue and 2 green marbles. If three marbles are picked at random, what is the probability that at least one is blue?

$$\frac{{28}}{{143}}$$
$$\frac{{115}}{{97}}$$
$$\frac{{28}}{{197}}$$
$$\frac{{115}}{{143}}$$

Q.5

A bag contains 21 toys numbered 1 to 21. A toy is drawn and then another toy is drawn without replacement.
Find the probability that both toys will show even numbers.

$$\frac{{5}}{{21}}$$
$$\frac{{9}}{{42}}$$
$$\frac{{11}}{{42}}$$
$$\frac{{4}}{{21}}$$

Q.6

Two dice are thrown simultaneously. Find the probability of getting a multiple of 2 on one dice and multiple of 3 on the other dice.

$$\frac{{5}}{{12}}$$
$$\frac{{11}}{{36}}$$
$$\frac{{5}}{{36}}$$
$$\frac{{13}}{{36}}$$

Q.7

What is the probability that a number selected from numbers 1, 2, 3, ......, 30, is prime number, when each of the given numbers is equally likely to be selected?

$$\frac{{9}}{{30}}$$
$$\frac{{8}}{{30}}$$
$$\frac{{10}}{{30}}$$
$$\frac{{11}}{{30}}$$

Q.8

In a charity show tickets numbered consecutively from 101 through 350 are placed in a box.
What is the probability that a ticket selected at random (blindly) will have a number with a hundredth digit of 2?

0.285
0.40
$$\frac{{100}}{{249}}$$
$$\frac{{99}}{{250}}$$

Q.9

You toss a coin AND roll a die. What is the probability of getting a tail and a 4 on the die?

$$\frac{{1}}{{2}}$$
$$\frac{{1}}{{6}}$$
$$\frac{{1}}{{8}}$$
$$\frac{{1}}{{12}}$$

Q.10

Two cards are drawn from a pack of well shuffled cards. Find the probability that one is a club and other in King.

$$\frac{{1}}{{13}}$$
$$\frac{{4}}{{13}}$$
$$\frac{{1}}{{52}}$$
$$\frac{{1}}{{26}}$$

Q.11

A committee of 3 members is to be selected out of 3 men and 2 women. What is the probability that the committee has at least 1 woman ?

$$\frac{{1}}{{10}}$$
$$\frac{{9}}{{20}}$$
$$\frac{{1}}{{20}}$$
$$\frac{{9}}{{10}}$$
None of these

Q.12

A speaks truth in 75% cases and B in 80% of the cases. In what percentage of cases are they likely to contradict each other, in narrating the same incident ?

5%
15%
35%
45%
None of these

Q.13

Four persons are chosen at random from a group of 3 men, 2 women and 4 children. The chance that exactly 2 of them are children, is-

$$\frac{{1}}{{9}}$$
$$\frac{{1}}{{5}}$$
$$\frac{{1}}{{12}}$$
$$\frac{{10}}{{21}}$$
None of thee

Q.14

A basket contains 6 blue, 2 red, 4 green, and 3 yellow balls. If three balls are picked up at random, what is the probability that none is yellow?

$$\frac{{3}}{{455}}$$
$$\frac{{1}}{{5}}$$
$$\frac{{4}}{{5}}$$
$$\frac{{44}}{{91}}$$
None of these

Q.15

In a box, there are 8 red, 7 blue and 6 green balls. One ball is picked up randomly. What is the probability that it is neither blue nor green ?

$$\frac{{2}}{{5}}$$
$$\frac{{3}}{{4}}$$
$$\frac{{7}}{{19}}$$
$$\frac{{8}}{{21}}$$
$$\frac{{9}}{{21}}$$

Q.16

Two dice are thrown simultaneously. What is the probability of getting two numbers whose product is even ?

$$\frac{1}{2}$$
$$\frac{3}{4}$$
$$\frac{3}{8}$$
$$\frac{5}{16}$$

Q.17

An urn contains 6 red, 4 blue, 2 green and 3 yellow marbles. If four marbles are picked up at random, what is the probability that 1 Is green, 2 are blue and 1 is red ?

$$\frac{13}{35}$$
$$\frac{24}{455}$$
$$\frac{11}{15}$$
$$\frac{1}{13}$$

Q.18

A bag contains 10 mangoes out of which 4 are rotten, two mangoes are taken out together. If one of them is found to be good, the probability that other also good is-

$$\frac{1}{3}$$
$$\frac{8}{15}$$
$$\frac{5}{18}$$
$$\frac{2}{3}$$

Q.19

A speaks truth in 60% cases B speaks truth in 70% cases. The probability that they will way say the same thing while describing a single event, is-

0.54
0.56
0.68
0.94
None of these

Q.20

A special lottery is to be held to select a student who will live in the only deluxe room in a hostel. There are 100 Year-III, 150 Year-II and 200 Year-I students who applied.
Each Year-III's name is placed in the lottery 3 times; each Year-II's name, 2 times and Year-I's name, 1 time. What is the probability that a Year-III's name will be chosen?

$$\frac{{1}}{{8}}$$
$$\frac{{2}}{{9}}$$
$$\frac{{2}}{{7}}$$
$$\frac{{3}}{{8}}$$

Q.21

If two dice are thrown together, the probability of getting an even number on one die and an odd number on the other is -

$$\frac{{1}}{{4}}$$
$$\frac{{1}}{{2}}$$
$$\frac{{3}}{{4}}$$
$$\frac{{3}}{{5}}$$

Q.22

The odds against an event are 5 : 3 and the odds in favour of another independent event are 7 : 5. Find the probability that at least one of the two events will occur.

$$\frac{{69}}{{96}}$$
$$\frac{{52}}{{96}}$$
$$\frac{{71}}{{96}}$$
$$\frac{{13}}{{96}}$$

Q.23

A bag contains 7 green and 5 black balls. Three balls are drawn one after the other. The probability of all three balls being green, if the balls drawn are not replaced will be:

$$\frac{{343}}{{1728}}$$
$$\frac{{21}}{{36}}$$
$$\frac{{12}}{{35}}$$
$$\frac{{7}}{{44}}$$

Q.24

Two teams Arrogant and Overconfident are participating in a cricket tournament. The odds that team Arrogant will be champion is 5 to 3, and the odds that team Overconfident will be the champion is 1 to 4. What are the odds that either Arrogant or team Overconfident will become the champion?

3 to 2
5 to 2
6 to 1
33 to 7

Q.25

The probability of success of three students X,Y and Z in the one examination are $$\frac{{1}}{{5}}$$, $$\frac{{1}}{{4}}$$ and $$\frac{{1}}{{3}}$$ respectively. Find the probability of success of at least two.

$$\frac{{1}}{{6}}$$
$$\frac{{2}}{{5}}$$
$$\frac{{3}}{{4}}$$
$$\frac{{3}}{{5}}$$

Q.26

Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn bears a number which is a multiple of 3 ?

$$\frac{3}{10}$$
$$\frac{3}{20}$$
$$\frac{2}{5}$$
$$\frac{1}{2}$$

Q.27

From a pack of 52 cards, two cards are drawn together at random. What is the probability of both the cards being kings?

$$\frac{1}{15}$$
$$\frac{25}{57}$$
$$\frac{35}{256}$$
$$\frac{1}{221}$$

Q.28

From a pack of 52 cards, 3 cards are drawn. What is the probability that one is ace, one is queen and one is jack?

$$\frac{{19}}{{5525}}$$
$$\frac{{21}}{{5525}}$$
$$\frac{{17}}{{5525}}$$
$$\frac{{16}}{{5525}}$$

Q.29

If the chance that a vessel arrives safely at a port is $$\frac{{9}}{{10}}$$ then what is the chance that out of 5 vessels expected at least 4 will arrive safely?

$$\frac{{14 \times {9^4}}}{{{{10}^5}}}$$
$$\frac{{15 \times {9^5}}}{{{{10}^4}}}$$
$$\frac{{14 \times {9^3}}}{{{{10}^4}}}$$
$$\frac{{14 \times {9^6}}}{{{{10}^5}}}$$

Q.30

P and Q sit in a ring arrangement with 10 persons. What is the probability that P and Q will sit together?

$$\frac{{2}}{{11}}$$
$$\frac{{3}}{{11}}$$
$$\frac{{2}}{{9}}$$
$$\frac{{4}}{{9}}$$

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