Addition Theorem of Probability for 2 Events

Q.

The probability of getting a bad egg in a lot of $400$ is $0.035$. The number of bad eggs in the lot is___

Q.

The probability of getting a bad egg in a lot of $400$ is $0.035$. The number of bad eggs in the lot is
(a) $7$
(b) $14$
(c) $21$
(d) $28$

Q.

A police officer is using a radar device to check motorists’ speeds.

Prior to beginning the speed check, the officer estimates that $40$ percent of motorists will be driving more than $5$ miles per hour over the speed limit.

Assuming that the police officer’s estimate is correct, what is the probability that among $4$ randomly selected motorists, the officer will find at least $1$ motorist driving more than $5$ miles per hour over the speed limit?

Q.

If $P\left(A\right)=\frac{2}{3}$, $P\left(B\right)=\frac{1}{2}$, and $P\left(AUB\right)=\frac{5}{6}$, then events $A$ and $B$ are

1. Mutually exclusive

2. Independent as well as mutually exhaustive

3. Independent

4. Dependent only on A

Q. Question 26
Two dice are thrown at the same time. Determine the probability that the difference of the numbers on the two dice is 2.

Q.

Of the members of three athletic teams in a certain school, $21$ are in the basketball team, $26$ in hockey team and $29$ in the football team. $14$ play hockey and basketball, $15$ play hockey and football, $12$ play football and basketball and $8$ play all the three games how many members are there in all?

1. $43$

2. $76$

3. $49$

4. None of these

Q.

You spin a spinner that has 8 equal-sized sections numbered 1 to 8. Find the theoretical probability of landing on the given section(s) of the spinner.
(i) section 1 (ii) odd-numbered section (iii) a section whose number is a power of 2. [4 MARKS]

Q.

If P(A) = 0.2, P(B’) = 0.6 and P(A$\cap$B)= 0.1. Find P(A$\cup$B).

Q. The sum of the probabilities of all the elementary events of an experiment is

Q.

A number from 1 to 10 is chosen at random. What is the probability of choosing 5 or an even number?

1. 2/5

2. 3/5

3. 1/5

4. 4/5

Q. A husband and a wife appear in an interview for two vacancies in the same post. The probability of husband`s selection is $\frac{1}{7}$ and that of wife's selection is $\frac{1}{5}$. What is the probability that only one of them will be selected?

1. $\frac{1}{7}$
2. $\frac{2}{7}$
3. $\frac{3}{7}$
4. $\frac{4}{7}$

Q. A single card is chosen at random from a standard deck of 52 playing cards. What is the probability that the card will be a club or a king?

1. $\frac{1}{4}$
2. $\frac{4}{13}$
3. $\frac{1}{13}$
4. $\frac{3}{13}$

Q.

A probability that in a year of the $22$nd century chosen at random, there will be $53$ Sundays is

1. $\frac{3}{28}$

2. $\frac{2}{28}$

3. $\frac{7}{28}$

4. $\frac{5}{28}$

Q. One of the two events must occur. If the chance of one is $\frac{2}{3}$ of the other, then odds in favour of the other are

1. 
2. 
3. 
4. 

Q.

Question 7(c)

Find the ratio of the following:

55 paise to Rs 1

Q. A number is selected from the first 25 natural numbers. What is the probability that it would be divisible by 4 or 7 ?

1. $\frac{1}{25}$
2. $\frac{9}{25}$
3. $\frac{9}{14}$
4. $\frac{6}{11}$

Q.

In a deck of cards, find the probability of getting a spade.

Q. A number is randomly selected from the first 40 natural numbers. What is the probability that the selected number is divisible by 5 or 7?

1. $\frac{8}{20}$
2. $\frac{17}{40}$
3. $\frac{7}{20}$
4. $\frac{3}{10}$

Q.

How do i calculate$\left(\right)+\left(\right)+\left(\right)=30$ in where i can repeat a number using $1,3,5,7,9,11,13,15$?

Q.

The chance of throwing at least $9$in a single throw with two dice is

1. $\frac{1}{18}$

2. $\frac{5}{18}$

3. $\frac{7}{18}$

4. $\frac{11}{18}$

Q. A bag contains $5$ red and $7$ black balls. If two balls are drawn successively without replacement, then the probability that the first one is red and the second is black is

1. $\frac{25}{132}$
2. $\frac{35}{132}$
3. $\frac{35}{144}$
4. $\frac{30}{144}$

Q.

In a class of 58 students, 20 follow cricket, 38 follow hockey and 15 follow basketball. Three students follow all the three games. How many students follow exactly two of these three games?

___

Q.

If E and F are mutually exclusive events, find the probability of (E’$\cup$ F’)

1. 0

2. 1

3. 0.5

4. 0.2

Q. A pack contains n cards numbered from 1 to n. Two consecutive numbered cards are removed from the pack and the sum of the numbers on the remaining cards is 1224. If the smaller of the numbers on the removed cards is k, then k-20 is equal to:

1. 5
2. 6
3. 7
4. 8

Q. For two independent events A and B, if P(A) = 0.5 and P(B) = 0.3 , then the value of $100P(A\cup B)$ =____.

1. 65
2. 90
3. 36
4. 75

Q.

Given that $P\left(AUB\right)=0.76$ and $P(AUB)=0.87$, find $P\left(A\right)$:

Q. A bag contains 6 red, 8 black and 4 white balls. A ball is drawn at random, What is the probability that the ball drawn is not black?

1. $\frac{5}{9}$
2. $\frac{3}{4}$
3. $\frac{1}{7}$
4. $\frac{3}{7}$

Q.

If E represents an event, P(E) + P(E’) = __

Q.

You spin a spinner that has 8 equal-sized sections numbered 1 to 8. Find the theoretical probability of landing on the given section(s) of the spinner.
(i) section 1 (ii) odd numbered section (iii) a section whose number is a power of 2. [4 MARKS]

Q. Question 39(ii)
A die has its six faces marked 0, 1, 1, 1, 6, 6. Two such dice are thrown together and the total score is recorded.
What is the probability of getting a total of 7?