Probability(11th Grade > Mathematics ) Questions and answers for exam Preparation

11th Grade > Mathematics

PROBABILITY MCQs

Total Questions : 30 | Page 3 of 3 pages

Question 21.

A set of integers is given as (3,6,8,14,17). What is the probability that a triangle can be constructed.?

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

Discuss Question

Answer: Option B. ->

\frac{3}{10}

:
B

Any 3 points can be selected in $^{5} C_{3}$ i.e 10 ways.

For forming a triangle sum of two sides should be greater than the $3^{r d}$ side.

Hence following set of integers can be selected

(3,6,8)

(6,8,17)

(8,14,17)

Hence P(Triangle is formed)= $\frac{3}{10}$

Question 22.

Letters of the word "EDUCATION" is arranged. What is the probability that vowels and consonants are in alphabetical order?

$\frac{1}{(5! \times 4!)}$
$\frac{1}{9!}$
$\frac{9}{9!}$
None of these

Discuss Question

Answer: Option A. ->

\frac{1}{(5! \times 4!)}

:
A

There are 5 vowels and 4 consonants.

Total ways to arrange: 9!

Vowels can be arranged in 5! ways out of which in $\frac{1}{5!}$ they are in alphabetical order.

Similarly for consonants.

Total Favorable ways: $\frac{9!}{(5! \times 4!)}$

Total ways: 9!

P(E)= $\frac{1}{(5! \times 4!)}$

Question 23.

There are 4 torn books in a lot consisting of 10 books. If 5 books are seleceted at random what is the probability of presence of 2 torn books among the selected?

$\frac{1}{3}$
$\frac{4}{21}$
$\frac{10}{21}$
$\frac{2}{7}$

Discuss Question

Answer: Option C. ->

\frac{10}{21}

:
C

Total Sample space: $^{10} C_{5} = 252$

Favorable cases: $^{4} C_{2} \times^{6} C_{3} = 120$

Hence P(E)= $\frac{120}{252} = \frac{10}{21}$

Question 24.

Of the 10 prizes 5 prizes are of category Platinum 3 of gold and 2 of silver and they are placed in an enclosure for an olympiad contest. The prizes are awarded by allowing winners to select randomly from the prizes remaining. When the 8th participant goes to collect the prize what the probability that last 3 prizes are 1 of platinum 1 of gold and 1 of silver?

$\frac{1}{5}$
$\frac{1}{4}$
$\frac{1}{3}$
$\frac{1}{10}$

Discuss Question

Answer: Option B. ->

\frac{1}{4}

:
B

Sample space: $^{10} C_{7}$ . because 7 prizes have already been selected= 120.

Favorable: $^{5} C_{4} \times^{3} C_{2} \times^{2} C_{1} = 30$ .

P(E)= $\frac{30}{120} = \frac{1}{4}$

Question 25.

The probability that a 'P and C' question wil be asked in IIT JEE is $\frac{2}{5}$ and probability question is uploaded is $\frac{4}{7}$ . If the probability of getting at least 1 is $\frac{2}{3}$ what is the probability that questions from both the topics are asked.

$\frac{17}{105}$
$\frac{16}{105}$
$\frac{1}{35}$
$\frac{6}{35}$

Discuss Question

Answer: Option A. ->

\frac{17}{105}

:
A

P(A U B)= P(A)+ P(B)- P(A intersection B)

$\frac{2}{3} = (\frac{2}{5}) + (\frac{4}{7}) - x$

$x = \frac{17}{105}$

Question 26.

A fortune teller has numbers from 1-7 in his box. He draws 3 numbers from it. What is the probability that the number picked is of alternate order as odd-even-odd or even-odd-even?

$\frac{1}{14}$
$\frac{2}{7}$
$\frac{9}{14}$
None of the above

Discuss Question

Answer: Option B. ->

\frac{2}{7}

:
B

Sample Space: $7 \times 6 \times 5 = 210$

odd-even-odd= $4 \times 3 \times 3 = 36$

even-odd-even= $3 \times 4 \times 2 = 24$

Total ways: 60

P(E)= $\frac{60}{210} = \frac{2}{7}$

Question 27.

Two cubes have their face painted as either red or blue color. 1st cube has 5 faces red and 1 face blue. The Probability that both the faces show same color on rolling is $\frac{1}{2}$ . How many red faces are present on the $2^{n d}$ cube.

Discuss Question

Answer: Option C. -> 3
:
C

Suppose x faces of cube 2 is red then 6-x will be blue.

P(RR or BB)= $\frac{5}{6} \times \frac{x}{6} + \frac{1}{6} \times \frac{(6 - x)}{6} = \frac{1}{2}$

$\frac{5 x}{36} + \frac{(6 - x)}{36} = \frac{1}{2}$

4x+6=18

x=3

Hence number of red faces is 3.

Question 28.

CSK lost the toss 13 out of 14 times. What is the probability of this event?

$\frac{3}{2^{14}}$
$\frac{5}{2^{14}}$
$\frac{7}{2^{13}}$
None of the above

Discuss Question

Answer: Option C. ->

\frac{7}{2^{13}}

:
C

13 losses from 14 can be selected in $^{14} C_{13}$ ways i.e.14

At any of the tosses only 2 events can happen win or loss hence total sample space: $2^{14}$

P(E)= $\frac{14}{2^{14}}$

Question 29.

A bag contains 'x' red balls '2x' white balls and '3x' black balls. 3 balls are drawn at random. The probability that all the balls drawn are of different colors is 0.3 .How many white balls are present in the bag?

Discuss Question

Answer: Option A. -> 2
:
A

P(All different)= $(^{x} C_{1}) \times (^{2 x} C_{1}) \times (^{3 x} C_{1}) / (^{6 x} C_{3})$

P(E)= $(6 x^{3}) \times \frac{6}{6 x} \times [(6 x - 1) \times (6 x - 2)] = \frac{3}{10}$

or, $\frac{3 x^{2}}{[(6 x - 1) \times (6 x - 2)]} = \frac{3}{10}$

$10 x^{2} = 18 x^{2} - 9 x + 1$

or, (x-1)(8x-1)=0

x can not be a fraction hence x=1

Total number of white balls= 2x=2

Question 30.

A maze with following pattern is given. An insect has to reach point R.It can only land only on R if it lands on the adjacent cubes. What is the probability of it reaching R.