Theoretical Probability

Q.

1 card is drawn from a well-shuffled deck of 52 cards. Find the probability of getting a red face card. [2 MARKS]

Q.

Harkeerat tosses 2 different coins simultaneously. Find the probability that she gets at least one head.

1. 

2. 

3. 

4. 

Q.

A card is drawn at random from a well shuffled pack of 52 cards. Find the probability that the card drawn has a prime number on it.

1. 1/13

2. 4/9

3. 4/13

4. 6/13

Q.

The probability that a marksman will hit a target is given as $\frac{1}{5}$. Then his probability of at least one hit in $10$ shoots is

1. $1-{\left(\frac{4}{5}\right)}^{10}$
2. $\frac{1}{5^{10}}$
3. $1-\left(\frac{1}{5^{10}}\right)$
4. None of these

1. $1-{\left(\frac{4}{5}\right)}^{10}$

2. $\frac{1}{5^{10}}$

3. $1-\left(\frac{1}{5^{10}}\right)$

4. None of these

Q.

A box contains 5 pencils, 16 pens and 1 eraser. What is the probability of drawing a pen from the box?

1. 

2. 

3. 

4. 

Q.

The probability that number selected at random from the numbers $1,2,3,4,5,6,7,8,...,100$ is a prime, is

1. $0.4$

2. $0.25$

3. $0.45$

4. $0.43$

Q. An unbiased die is thrown once. The probability of getting an even number is

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

Q.

1 card is drawn from a well-shuffled deck of 52 cards. Find the probability of getting a red face card. [2 MARKS]

Q.

What are the odds against choosing a blue marble from a bag that contains two blue marbles, one green marble, seven white marbles, and four red marbles?

1. $12:2$

2. $2:14$

3. $14:2$

4. $10:2$

Q. Three coins are tossed simultaneously $100$ times with the following frequencies of different outcomes- no head$-14$ one head$-38$ two heads$-36$ three heads$-12$ if the three coins are simultaneously tossed again, compute the probability of: (1). $2$ heads coming up. (2). $3$ heads coming up. (3). at least one head coming up. (4).getting more heads than tails. (5). getting more tails than heads.

Q. Number of heads obtained when a coin is tossed 700 times is ________.

1. 350
2. 500
3. 0
4. Can't be determined

Q. When we pick a fruit from the basket, the total number of possible outcomes is .

1. 2
2. 1
3. 3

Q.

In a simultaneous toss of n coins, find the probability that no head occurs.

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

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

3. $\frac{1}{2^n}$

4. $\frac{1}{n^2}$

Q.

We know that Probability of an event E, written as
P(E)
$=\frac{\text{Number of outcomes favourable to E(m)}}{\text{Number of all possible outcomes of the experiment(n)}}$.

Which of the following options correctly explains the relationship between m and n?

1. $m=n>0$

2. $m\ge 0,n>0,m\le n$

3. $m\ge 0\ge n$

4. $0\ge m\ge n$

Q. One bag contains $3$ red $5$ black balls. Another bag contains $6$ red $4$ black balls. A ball is transferred from first bag to the second bag and then a ball is drawn from the second bag. Find the probability that the ball drawn is red.

Q. There are 6 marbles in a box with numbers from 1 to 6 marked on each of them.
What is the probability of drawing a marble with number 5?

Q. An electrical shopkeeper purchases bulbs fromthree manufacturers A, B, C. He purchases $25$%of his stock from A, $45$% from B and $30$% from C.In the past purchases he found $2$% of Cs bulbs, 1% of Bs bulbs, 1% of As bulbs were defective.Assuming that, the shopkeeper chooses a bulband found it to be defective
LIST-I LIST-II
A) The probability of choosing 1) 0.0025
A and purchasing a defective
bulb from it is
B) The probability of choosing 2) 0.0045
B and purchasing a defective
bulb from it is
C) The probability of choosing 3) 0.0060
C and purchasing a defective
bulb from it is
D) The probability that the 4) 0.65
defective bulb was purchased
from C is 5) 0.46

1. $4523$
2. $2315$
3. $5231$
4. $1235$

Q. The mathematical study of randomness is called probability theory.

1. True
2. False
3. Partly true
4. None of above

Q.

The scores of a batsman in the last 10 innings were 10, 0, 25, 9, 24, 81, 28, 2, 1, and 59. What is the probability that he will score more than 30 runs in his next innings (in decimal)?

__

Q. A bag contains $3$ red balls, $5$ black balls and $4$ white balls. A ball is drawn at random from the bag. The probability that the ball drawn is white is $\frac{1}{3}$

Q. An experiment is a method that can be repeated infinitely and has a well-defined set of possible outcomes.

1. True
2. False

Q. The theory of probability involves the study of a

1. Luck
2. Haphazard phenomena
3. Random phenomena
4. None of above

Q. A die is thrown twice. The probability that $5$ will not come up either of the time is

1. $\frac{25}{36}$
2. $\frac{35}{36}$
3. $\frac{1}{36}$
4. $\frac{11}{36}$

Q.

Two coins are tossed simultaneously. The probability of getting at least one head is __. Give the answer up to 2 decimal places

Q. Rohan and Shalu are playing with 5 cards as shown in the figure. What is the probability of Rohan picking a card without seeing, that has the number 2 on it?

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

Q. Match the given situations with their total number of outcomes.

1. 6
2. 2
3. 8

Q.

The above pie chart depicts the percentage of students being girls and boys in the mechanical branch of NIT Trichy college. If the red coloured portion represents the boys percentage and the total number of students be 100 then what is the probability of a student being picked at random being a girl?

1. $\frac{1}{25}$

2. $\frac{25}{99}$

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

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

Q.

A card is drawn at random from a well-shuffled deck of playing cards. Find the probability that the card drawn is either a king or a queen.

Q. Which of the following is the probability of getting an even number by throwing a dice?

Q. Is "The number of points scored during a basketball game." discrete or continuous?