Complementary Events

Q.

A six-faced dice is so biased that it is twice as likely to show an even number as an odd number when thrown. It is thrown twice. The probability that the sum of two numbers thrown is even, is

1. $\frac{1}{12}$

2. $\frac{1}{6}$

3. $\frac{1}{3}$

4. $\frac{5}{9}$

Q. Question 7
It is given that in a group of 3 students, the probability of 2 students not having the same birthday is 0.992. What is the probability that the 2 students have the same birthday?

Q. By what number should (−240) be divided to obtain 16?

Q.

Find:

(i) 2.5 × 0.3 (ii) 0.1 × 51.7 (iii) 0.2 × 316.8

(iv) 1.3 × 3.1 (v) 0.5 × 0.05 (vi) 11.2 × 0.15

(vii) 1.07 × 0.02 (viii) 10.05 × 1.05 (ix) 101.01 × 0.01

(x) 100.01 × 1.1

Q. Find the third proportional to:

(i) 8 and 12
(ii) 12 and 18
(iii) 4.5 and 6

Q. Express $\frac{84}{-147}$ as a rational number with denominator

(i) 7
(ii) −49

Q.

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

1. 0.3

2. 0.85

3. Cannot be determined

4. 0.35

Q. By what number should $-4\frac{3}{8}$ be divided to obtain $-3\frac{1}{2}$?

Q. Question 5
If P(E) = 0.05, what is the probability of ‘not E’?

Q. The probability of an event is never a number.

1. True
2. False

Q. Divide:
(i) 459.5 by 100
(ii) 74.3 by 100
(iii) 5.8 by 100
(iv) 0.7 by 100
(v) 0.48 by 100
(vi) 0.03 by 100

Q. The probability of an event is never a number.

1. True
2. False

Q. A rope of length $13\frac{1}{2}$ m has been divided into 9 pieces of the same length. What is the length of each piece?

Q.

2.5 x 2.5 =

1. 625

2. 62.5

3. 0.625

4. 6.25

Q.

Convert the base 10 numbers into base 2 by division method.

(1) 2

(2) 6

(3) 18

(4) 22

(5) 30

(6) 44

(7) 51

(8) 63

(9) 77

(10) 100

Q.

40.5 g + 62.4 g = ?

1. 1029 kg

2. 0.1029 kg

3. 0.1029 g

4. 10.29 g

Q.

Fill in the blanks with suitable signs = or ≠.

Q. By what number should $6\frac{2}{9}$ be divided to obtain $4\frac{2}{3}$?

Q. Simplifiy 30.94÷0.7

Q.

1. 9/8 litres

2. 9/4 litres

3. 11/4 litres

4. 11/2 litres

Q. If the cost of a notebook is Rs $7\frac{3}{4}$, how many notebooks can be purchased for Rs $69\frac{3}{4}$ ?

Q. Divide:

(i) 0.196 by 1.4
(ii) 39.168 by 1.2
(iii) 0.228 by 0.38

Q. Find the fourth proportional to the numbers:

(i) 8, 36, 6
(ii) 5, 7, 30
(iii) 2.8, 14, 3.5

Q.

Divide 457.25 by 1000.

1. 4.5725

2. 0.45725

3. 45.725

4. 4572.5

Q. Mark (✓) against the correct answer
By what number should $1\frac{3}{4}$ be divided to get $2\frac{1}{2}$?
(a) $\frac{3}{7}$
(b) $1\frac{2}{5}$
(c) $\frac{7}{10}$
(d) $1\frac{3}{7}$

Q.

If P(E) and P(E’) are the probabilities of two complementary events, then which of the following is always true?

1. $P\left(E\right)+P\left(E^{\prime }\right)=1$

2. $P\left(E\right)+P\left(E^{\prime }\right)=0$

3. $P\left(E\right)=P\left(E^{\prime }\right)$

4. $P\left(E\right)+P\left(E^{\prime }\right)=\frac{1}{2}$

Q.

Question 76(iii)

The drawing below (figure), show angles formed by the goalposts at different positions of a football player. The greater the angle the better chance the player has of scoring a goal, e.g. The player has a better chance of scoring a goal from position A than from position B.

Estimate at least two situations, such that the angles formed by different positions of two players are the complement to each other.

Q. Divide:
(i) 142.45 by 10
(ii) 54.25 by 10
(iii) 3.45 by 10
(iv) 0.57 by 10
(v) 0.043 by 10
(vi) 0.004 by 10

Q.

If P(A) = 0.15, then P(not A) =

1. 0.35

2. 0.3

3. 0.85

4. Cannot be determined

Q.

The probability of it being a rainy day is 0.75, then the probability of it not being a rainy day is ___.

1. 0.25

2. 0.35

3. 0.05

4. 2.5