Mathematics Test

Result

Mathematics Test - 5

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Weekly Quiz Competition

Question 1
3 / -1

If A and B are independent events of a random experiments such that

A
1/4

B
1/3

C
5/7

D
2/3

Solution

Since, A & B are independent events.
Question 2
3 / -1

Given two mutually exclusive events A and B such that P(A)=0.45 and P(B)=0.35, Find P(A∩B)

A
63/400

B
0.8

C
63/200

D
0

Solution

P(A)=0.45,

P(B)=0.35 (events are mutually exclusive)

P(A∩B)=0
Question 3
3 / -1

A problem in mathematics is given to 3 students whose chances of solving individually are 1/2,1/3 and 1/4 The probability that the problem will be solved at least by one is

A
1/4

B
1/24

C
23/24

D
3/4

Solution
Question 4
3 / -1

A team of 8 couples, (husband and wife) attend a lucky draw in which 4 persons picked up for a prize. The probability that there is at least one couple is

A
11/39

B
15/39

C
14/39

D
12/39

Solution

8 couples are there out of which 4 persons are picked for a prize.

P (At least one couple in 4)=1−P ( No Couple in 4)
Question 5
3 / -1

A pair of a dice thrown, if 5 appears on at least one of the dice, then the probability that the sum is 10 or greater, is

A
11/36

B
2/9

C
3/11

D
1/12

Solution

Favourable cases of getting 10 or greater than 10, if 5 appears on atleast one of dice.

= {(5, 6), (6, 5), (5, 5)}

Number of favourable cases =3

Total number of cases =6×6=36

∴ Required probability = 3/36 = 1/12
Question 6
3 / -1

A
4/11

B
5/11

C
6/11

D
7/17

Solution
Question 7
3 / -1

Coins are marked with a,b;b,c;c,a. All are tossed, probability that two of the faces shows the same letter is

A
3/8

B
1/8

C
3/4

D
1/4

Solution

Total outcomes =2 × 2 × 2 = 8

Unfavourable outcomes =2 = 2 , , i.e. either (a,b,c) or (b,c,a)

Hence, required probability = 1 - faces does not show same letter
Question 8
3 / -1

A box contains tickets numbered 1 to N. n tickets are drawn from the box with replacement. The probability that the largest number on the tickets is k is

A

B

C
0

D
None of these

Solution

Since the tickets are drawn with replacement, the same ticket may be repeated. Since the largest ticket is k, the tickets chosen are from 1 to k.

Total no. of ways of doing it = kⁿ

However, k may or may not have been drawn.

No. of ways of choosing numbers from 1 to (k - 1) = (k - 1)ⁿ
Question 9
3 / -1

Probability that in the toss of two dice we obtain an even sum or a sum less than 5, is

A
1/2

B
1/6

C
2/3

D
5/9

Solution

Let A be the event of obtaining an even sum and B be the event of obtaining a sum less 5

Then, we have to find P(A∪B).Since, A,B are not mutually exclusive, we have

P(A∪B)=P(A)+P(B)−P(A∩B)

[Since, there are 18 18 ways to get an even sum and 6 6 ways to get a sum less than 5 ie. (1,3), (3,1), (2,2), (1,2), (2,1),(1,1) and 4 ways to get an even sum less than 5, ie,(1,3), (3,1), (2,2), (1,1).]
Question 10
3 / -1

Six faces of an unbiased die are numbered with 2,3,5,7,11 & 13. If two such dice are thrown, then the probability that the sum on the uppermost faces of the dice is an odd number, is

A
5/18

B
5/36

C
13/18

D
25/36

Solution

The sum of two numbered on a dice is odd only, when one number is odd and second is even.

∴ Required probability

= 2× Probability of odd number × Probability of even number

[ ∵ Here, we multiply by 2 because either the even number is on first or on second dice.]