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Test: Probability and Statistics - 9 - Mathematics MCQ


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20 Questions MCQ Test - Test: Probability and Statistics - 9

Test: Probability and Statistics - 9 for Mathematics 2024 is part of Mathematics preparation. The Test: Probability and Statistics - 9 questions and answers have been prepared according to the Mathematics exam syllabus.The Test: Probability and Statistics - 9 MCQs are made for Mathematics 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Probability and Statistics - 9 below.
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Test: Probability and Statistics - 9 - Question 1

If a student is likely to choose any of the four choices with equal probability in a multiple-choice examination with five questions then the probability that the student answer at least four questions correctly is

Detailed Solution for Test: Probability and Statistics - 9 - Question 1

P(Answering at least 4 questions correctly)

Test: Probability and Statistics - 9 - Question 2

Let  where a, b, c are chosen randomly from the set {1,2,3,4,5}. The probability that P is singular is

Detailed Solution for Test: Probability and Statistics - 9 - Question 2

 P will be singular if |P| = 0
⇒ c-ab = 0
cases in favour are

Thus 10 out of 5 x 5 x 5 = 125 cases are in favour, so

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Test: Probability and Statistics - 9 - Question 3

Subway trains on a certain line run every half hour between midnight and six in the morning. Find the probability that a person entering the station at a random time during this period will have to wait at least twenty minutes. 

Detailed Solution for Test: Probability and Statistics - 9 - Question 3

Waiting time of person will lie in the range (0,30) and in this range favourable portion is (20, 30), so the required probability is the ratio of the time interv l's length i.e. 

Test: Probability and Statistics - 9 - Question 4

In a certain office, 1/3 of the workers are women, 1 /2 of the women are married and 1 /3 of the married women have children. If 3/4 of the men are married and 2/3 of the married men have children, what part of workers are without children?

Detailed Solution for Test: Probability and Statistics - 9 - Question 4

Part, of workers having children

Test: Probability and Statistics - 9 - Question 5

A man has 5 coins, two of which are double - headed, one is double - tailed and two are normal. He shuts his eyes, picks a coin at random, and tosses it. The probability that the lower face of the coin is a head is

Detailed Solution for Test: Probability and Statistics - 9 - Question 5

Required probability = P(DH | H) + P(DT | H)

Test: Probability and Statistics - 9 - Question 6

A and B are independent witnesses in a case. The probability that A speaks the truth is 'x' and that B speaks the truth is ‘y'. If A and B agree on a certain statement, the probability that the statement is true is

Detailed Solution for Test: Probability and Statistics - 9 - Question 6

Prob. (statement is true | Agreement)


Note: Agreement can be there if both are speaking truth or both are telling a lie.

Test: Probability and Statistics - 9 - Question 7

Let A and B be two events such that  Then events A and B

Detailed Solution for Test: Probability and Statistics - 9 - Question 7



so, A and B are independent but not equally likely.

Test: Probability and Statistics - 9 - Question 8

The probability that a man who is 85 yrs. old will die before attaining the age of 90 is 1 / 3. A1, A2, A3 and A4 are four persons who are 85 yrs. old. The probability that A1 will die before attaining the age of 90 and will be the first to die is

Detailed Solution for Test: Probability and Statistics - 9 - Question 8

Required probability = P[at least one person dies before 90 days) x P(first person to die is A1)

Test: Probability and Statistics - 9 - Question 9

Find the value of k in the equation x3 -6x2 + kx + 64 = 0, if it is known that the roots of the equation are in geometric progression.

Detailed Solution for Test: Probability and Statistics - 9 - Question 9

Let a/r, a and ar be the three roots, then

Now, sum of the roots taken two at a time
2(-4) + (-4) (8) + 8(2) = K
⇒ K = -24

Test: Probability and Statistics - 9 - Question 10

An anti aircraft gun can take a maximum of four shots at an enemy plane moving away from it. The probabilities of hitting the plane at first, second, third and fourth shot are 0.4, 0.3, 0.2 and 0.1 respectively. The probabality that the gun hits the plane then is

Detailed Solution for Test: Probability and Statistics - 9 - Question 10

Required probability

Test: Probability and Statistics - 9 - Question 11

A bag contains 4 while and 3 black balls and a second bag contains 3 white and 3 black balls. If a ball is drawn from each of the bags, then the probability that both are of same colour is:

Detailed Solution for Test: Probability and Statistics - 9 - Question 11

Required probability that both will be of same colour is that both ese white or both are black.

Test: Probability and Statistics - 9 - Question 12

The probability of getting atleast 6 head in 8 trials is:

Detailed Solution for Test: Probability and Statistics - 9 - Question 12

Probability of getting 6 heads in 8 trials is,

Test: Probability and Statistics - 9 - Question 13

Bag A contain 10 bulbs in which 3 bulbs are defective. 2 bulbs are drawn. What is the probability of the both bullps being non-defective?

Detailed Solution for Test: Probability and Statistics - 9 - Question 13

Out of 10 bulbs, 3 are deflective, hence 7 will be non-defective, so the required probability is

Test: Probability and Statistics - 9 - Question 14

Prob. of getting an odd number or a no. less than 4 in throwing a dice is :

Detailed Solution for Test: Probability and Statistics - 9 - Question 14

The number which is odd or less than 4 is in our favour. So out of 6 numbers on the dice 4 numbers are in our favour (i.e. 1, 2, 3, 5) So probability 

Test: Probability and Statistics - 9 - Question 15

Given A and B are mutually exclusive events. If P(B) = 0.15
 P(A) is equal to 

Detailed Solution for Test: Probability and Statistics - 9 - Question 15


P = ( A ) + P(B)
[as A and are mutually exclusive]

Test: Probability and Statistics - 9 - Question 16

In a pack of 52 cards, the probability of drawing at random such that it is diamond or card king is:

Detailed Solution for Test: Probability and Statistics - 9 - Question 16

Out of 52 cards 13 are diamonds. We have 4 king cards from each suit. A card will be either diamond or a king has 13 + 4 -1 = 16 possibilities. So, required probaility = 16/52 = 4/13

Test: Probability and Statistics - 9 - Question 17

Given A and Bare mutually exclusive events.if: P(A ∪ B) = 0.8, P(B) = 0.2 then P(A) is equal to

Detailed Solution for Test: Probability and Statistics - 9 - Question 17


= P(A) + P(B) [as A and are mutually exclusive]

Test: Probability and Statistics - 9 - Question 18

Two dice are thrown once the probability of getting a sum 9 is given by :

Detailed Solution for Test: Probability and Statistics - 9 - Question 18

For sum of 9, the following values of the number on the faces are possible (3, 6) ; (4, 5) ; (5, 4) and (6, 3)
So, probability of getting sum 9 is

Test: Probability and Statistics - 9 - Question 19

In a pack of 52 cards. Two cards are drawn at random. The probability that it being club card is:

Detailed Solution for Test: Probability and Statistics - 9 - Question 19

As out of 52 cards 13 are clubs, so, the probaility that 2 cards selected at random are clubs is

Test: Probability and Statistics - 9 - Question 20

If P(A∩B) is equal to 19/60 then P(A∪B) is equal to

Detailed Solution for Test: Probability and Statistics - 9 - Question 20

By De Morgan's Law 

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