Probability(Quantitative Aptitude ) Questions and answers for exam Preparation

Quantitative Aptitude

PROBABILITY MCQs

Probability, Probability I

Total Questions : 775 | Page 6 of 78 pages

Question 51. The probability of winning a game is

\frac{2}{5}

, the probability of losing is__. (in decimal form)

Discuss Question

:
Winning or losing a game are complementary events. We know that, for complementary events, P(A) + P(notA) = 1.
Thus, if P(winning) =

\frac{2}{5}

Then, P(losing) = 1 -

\frac{2}{5}

\Rightarrow

P(losing) =

\frac{3}{5}

= 0.6.

Question 52. From a set of 17 cards, numbered 1, 2, ..., 17, one card is drawn at random. What is the probability that number on the drawn card is a multiple of 3 or 7 ?

Discuss Question

Answer: Option B. -> 717
:
B
The total number of possibleoutcomes(counting of the cards from 1to 17) = 17
Favourable outcomes are3, 6, 7, 9, 12, 14 and 15.

∴

No. offavourable outcomes = 7
Let

E

be the event of getting a multiple of 3 or 7.

∴

Probability P(E)

\frac{Number of outcomes favorable to E}{Number of all possible outcomes of the experiment} = \frac{7}{17}

Question 53. If P(A) and P(not A) are complementary events and P(A) = 0.15, then P(not A) = ?

0.35
0.3
0.85
Cannot be determined

Discuss Question

Answer: Option C. -> 0.85
:
C
Given, P (A) = 0.15
As, P(A) and P(not A) are complementary events, P(A) + P(not A) = 1
P (not A) = 1 – P (A) = 1 – 0.15 = 0.85

Question 54. You are given a dart board of radius R cm. What is the probability that you hit the bull's eye of radius r cm?

r2R2
rR
Rr
1

Discuss Question

Answer: Option A. -> r2R2
:
A
Area of board =

π

R^{2}

Area of bull's eye =

π

r^{2}

Here, weshalluse the concept of geometric probability as the number of outcomes are not finite.

The probability of hitting the bull's eye

= \frac{Area of the bull's eye}{Area of the board}

\frac{π . r^{2}}{π . R^{2}}

\frac{r^{2}}{R^{2}}

Question 55. What is the probability that the minute and hour hands of a clock will form an acute angle at any given time?

P ≤ 0.25
P
P = 0.5
P > 0.5

Discuss Question

Answer: Option B. -> P
:
B
The number of times in a period of 12 hours the hands of the clock will form an acute angle will be the same as that for obtuse angle. So, you would think that the probability is

\frac{1}{2}

. But if you take into account the number of times when the hands are alligned (

0^{\circ}

), hands are at right angles and hands are facing in opposite directions (

180^{\circ}

), then the probability would be slightly less than 0.5.

Question 56. A book has pages numbered from 1 to 85. What is the probability that the sum of the digits on the page is 8, if a page is chosen at random?

Discuss Question

Answer: Option C. -> 985
:
C
Total number of pages in the book = 85
Favorable outcomes are:8, 17, 26, 35, 44, 53, 62, 71, 80.

∴

No. of favorable outcomes = 9
Let

E

be the event of gettingsum of the digits on the page is 8.

Probability P(E)

\frac{Number of outcomes favorable to E}{Number of all possible outcomes of the experiment} = \frac{9}{85}

Question 57. A bag contains 100 identical marble stones numbered from 1 to 100. What is the probability of drawing a marble having a number divisible by both 4 and 5?

Discuss Question

Answer: Option D. -> 120
:
D
Numbers divisible by 4 and 5 both = 20, 40, 60, 80, 100.
Hence P =

\frac{Favourable outcomes}{Total outcomes}

\frac{5}{100}

\frac{1}{20}

\frac{1}{20}

Question 58. If a coin is tossed 3 times, what is the probability of getting a tail each time?

Discuss Question

Answer: Option A. -> 18
:
A
If a coin tossed thrice, the total possible outcomes = {HHH, HHT, HTT, HTH, THH, TTH, THT, TTT}.
= 8
Number of cases of getting tail each time = {TTT}
= 1
The probability of getting tail each time =

\frac{Number of favourable cases}{total possible outcomes}

\frac{1}{8}

Question 59. Sum of probabilities of all outcomes in an experiment is__

Discuss Question

:
The sum of the probabilities of all the elementary events of an experiment is 1.

Question 60. State whether the given statement is true or false:
A bag contains 4 red and 8 blue marbles. A marble is drawn at random. The probability of drawing red is