Complement of an Event

Q.

If three coins are tossed, find the probability of getting at least one tail.

Q. Question 1 (ii)
Complete the following statements:
The probability of an event that cannot happen is ___. Such an event is called ___.

Q.

Three coins are tossed. If one of them shows tail, then the probability that all three coins show tail is

1. $\frac{1}{7}$

2. $\frac{1}{8}$

3. $\frac{2}{7}$

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

Q. Two dice are thrown at the same time. Find the probability of getting different numbers on the dice.

1. $\frac{5}{6}$
2. $\frac{2}{3}$
3. $\frac{1}{6}$
4. $\frac{1}{3}$

Q.

If any four numbers are selected and they are multiplied then the probability that last digit in the product will be $1,3,5\mathrm{or}7$ is

1. $\frac{4}{625}$

2. $\frac{18}{625}$

3. $\frac{16}{625}$

4. none of these

Q.

If three coins are tossed, find the probability of getting, at least, one tail.

1. 5/8

2. 3/8

3. 7/8

4. 1/8

Q. Which of the following options is correct?

1. $P\left(E\right)=1+P\left(\overline{E}\right)$
2. $P\left(\overline{E}\right)-P\left(E\right)=1$
3. $P\left(E\right)+P\left(\overline{E}\right)=1$
4. None of these

Q. In class 10A, there are 30 boys and 20 girls. In 10B, there are 15 boys and 25 girls. One student is to be selected from each class.

i. What is the probability of both being girls?
ii. What is the probability of both being boys?
iii. What is the probability of one boy and one girl?
iv. What is the probability of at least one boy?

Q.

If the probability of winning a game is 0.995, then the probability of losing is

1. 1

2. 0.005

3. 0.05

4. 0

Q.

From a bag containing $5$ nickels, $8$ dimes, and $7$ quarters, $5$ coins are drawn at random and all at once. What is the probability of getting $2$ nickels, $2$ dimes, and $1$ quarter?

Q. A bomber want to destroy a bridge.Two bombs are sufficient to destroy it .If four are dropped, what is the probability that it is destroyed, if the chance of a bomb hitting the target is 0.4

Q. E is the event of 'getting an even prime number' on rolling a dice once. The probability of it's complementary event is .

1. $\frac{1}{6}$
2. $\frac{2}{3}$
3. $\frac{1}{3}$
4. $\frac{5}{6}$
5. 1

Q. The figure shows a circle with centre O and radius 8 cm. $\angle$ BOD =${72}^{\circ }$. The radius of the smaller circle is 4 cm. A point is selected randomly inside the larger circle, find the probability that the point lies neither inside the smaller circle nor inside the sector.

1. $\frac{13}{20}$
2. $\frac{3}{5}$
3. $\frac{1}{2}$
4. $\frac{11}{20}$

Q. Two dice are thrown at the same time.The probability of getting different numbers on the dice is .

1. $\frac{2}{3}$
2. $\frac{5}{6}$
3. $\frac{1}{6}$

Q. If the probability of hitting a target is 0.99, then the probability of not hitting the target is ____.

1. 
   1

2. 
   1/2

3. 
   0.01
4. 
   0.1

Q. A six face dice is marked with the numbers 1, 2, 3, 4, 5 and 6. What is the probability of getting a number which is not even?

1. $\frac{2}{3}$
2. $\frac{3}{4}$
3. $\frac{1}{2}$
4. $\frac{1}{3}$

Q.

What is an example of conditional probability?

Q. Match the following events with their corresponding complementary event on rolling a die once.

1. Odd number
2. {4, 5, 6}
3. {1, 4, 5, 6}
4. {1}

Q.

Three letters are randomly selected from the $26$ capital letters of the English alphabet. What is the probability that letters A will not be included in the choice?

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

2. $\frac{23}{26}$

3. $\frac{12}{13}$

4. $\frac{25}{26}$

Q. If the probability of hitting a target is 0.99, then the probability of not hitting the target is ____.

1. 
   1

2. 
   1/2

3. 
   0.01
4. 
   0.1

Q. Cards bearing numbers $2,4,6,8,10,12,14,16,18$ and $20$ are kept in a bag. A card is drawn at random from the bag. Find the probability of getting a card which is
(i) a prime number
(ii) A number is divisible by 4.

Q. Two aeroplanes I and II bomb a target in succession. The probabilities of aeroplanes I and II scoring a hit correctly are 0.3 and 0.2 respectively. The second plane will bomb only if the first plane misses the target. Find the probability that the target is hit by the secondplane.

Q. A six face dice is marked with the numbers 1, 2, 3, 4, 5 and 6. The probability of getting a number which is not even .

1. $\frac{2}{3}$
2. $\frac{3}{4}$
3. $\frac{1}{2}$

Q.

Which of the following pair of events are complementary events with respect to rolling of a die once ?

1. Getting a '5' or '6' or getting 1, 2, 3 or 4.

2. Getting an even number or an odd number.

3. Getting a number divisible by 2 or 3 or getting number 1 or 5.

4. Getting a number divisible by '1' or getting a number greater than '6'.

Q. Two dice are thrown simultaneously. The probability of getting a doublet is:

[1 mark]

1. $\frac{1}{6}$
2. $\frac{2}{3}$
3. $\frac{1}{3}$
4. $\frac{1}{2}$

Q. In each of the following experiments write the sample space S, number of sample points n(S), events P, Q, R using set form and n(P), n(Q) and n(R).
Find the events among the events defined above which are:
complementary events, mutually exclusive events and exhaustive events

(i) Three coins are tossed simultaneously:
P is the event of getting at least two heads.
Q is the event of getting no head.
Q is the event of getting head on second coin.

Q.

Two dice are thrown, find the probability of each of the following events:
P is the event that the sum of the scores on the uppermost faces is a multiple of 6.
Q is the event that the sum of the scores on the uppermost faces is at least 10.
R is the event that same score on both dice.

Q. If two unbiased coins are tossed once, what is the probability of getting::
All heads

Q.

The letters of the word AUDIT are rearranged.

What is the probability of (i) A new word starting with a vowel (ii) A new word starting with a consonant?

Are one and two complementary events?

Q. An event E is defined as 'getting a number that is a multiple of '1' on rolling a dice once. The probability of the complement event of E is .

1. 0
2. 1
3. $\frac{1}{2}$
4. $\frac{2}{3}$
5. $\frac{1}{4}$