Theoretical Probability

Q.

A die is thrown once, the probability of getting a composite number on the die is

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

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

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

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

Q.

Find the probability of obtaining a number less than $4$ when a die is thrown.

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

B. $\frac{1}{5}$

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

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

Q.

What does at least mean in probability?

Q.

A problem in Mathematics is given to three students, A, B, C, and their respective probability of solving the problem is $\frac{1}{2},\frac{1}{3}$ and $\frac{1}{4}$. The probability that the problem is solved is

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

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

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

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

Q.

Find the probability of getting $53$ Fridays in a leap year $?$

Q.

Find the probability of getting $53$ Sundays in a non-leap year.

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

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

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

4. $\frac{1}{9}$

Q.

A card is drawn from a well shuffled deck of $52$ cards. what is the probability of getting a red queen card.

Q.

Let a computer program generate only the digits $0$and $1$ to form a string of binary numbers with a probability of occurrence of $0$at even places be $\frac{1}{2}$ and probability of occurrence of $0$at the odd place be $\frac{1}{3}$. Then the probability that $10$ is followed by $01$ is equal to :

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

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

3. $\frac{1}{9}$

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

Q.

From a group of $8$ boys and $3$ girls, a committee of $5$ members to be formed. Find the probability that $2$ particular girls are included in the committee.

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

2. $\frac{2}{11}$

3. $\frac{6}{11}$

4. $\frac{8}{11}$

Q.

A die is tossed thrice.

Find the probability of getting an odd number at least once.

Q. What is the probability of NOT getting purple in the spinner?

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

Q.

Question 10 (i)
A piggy bank contains hundred 50 p coins, fifty Re. 1 coins, twenty Rs. 2 coins and ten Rs. 5 coins. If it is equally likely that one of the coins will fall out when the bank is turned upside down, what is the probability that the coin will be a 50 p coin?

Q.

Tina and Seenu are friends. What is the probability that both will have (i) different birthdays (ii) the same birthday? (ignoring leap years)

1. $\frac{364}{365},\frac{1}{365}$

2. $\frac{1}{365},\frac{364}{365}$

3. $\frac{2}{365},\frac{363}{365}$

4. $\frac{363}{365},\frac{2}{365}$

Q.

What is the probability of getting all tails?

Q.

A fair die is rolled once. [4 MARKS]
(i) What is the probability of getting a multiple of 2?
(ii) What is the probability of getting a prime number?

Q.

A survey of $250$ boys in a school was conducted and it was found that $110$ like coffee and $140$ do not like coffee. Out of these boys, one boy is selected at random. What is the probability that the selected boy: (i) likes coffee or (ii) does not like coffee?

Q.

$P\left(A\right)=p,P\left(B\right)=2p,P\left(\text{Exactly one out of A and B occurs}\right)=\frac{5}{9}$. What will be the maximum value of $p$?

Q.

In an urn, there are 30 blue balls, 20 red balls and x green balls and y black balls. A ball is taken at random from the urn. The probability that the chosen ball is not red in colour is $\frac{3}{4}$ and it is known that the number of black balls is twice the number of green balls. Find the value of y-x.

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Q.

In an urn, there are 30 blue balls, 30 black balls and 30 red balls. If a ball is picked from the urn then find the probability that the ball is blue?

1. 

2. 

3. 

4. 

Q. What is the probability of rolling a fair die and getting an even number?

1. $\frac{1}{6}$
2. $\frac{1}{2}$
3. $\frac{5}{6}$
4. None of the above

Q.

Krishna tosses 2 fair coins simultaneously. What is the probability he gets at least one head?

1. 0.5

2. 0.75

3. 1

4. 0.25

Q. How do you write the probability value of 0.02 in a percentage format?

1. $20\%$
2. $200\%$
3. $2\%$
4. $0.02\%$

Q. Stacy bought a pack of lotus seeds, and planted $50$ seeds. Out of $50$ seeds, only $23$ grew into plants. What is the probability that the next seed stacy plants will grow into a plant?

1. $\frac{23}{51}$
2. $\frac{23}{50}$
3. $\frac{24}{51}$
4. None of the above

Q.
The missing data in the frequency table is

1. 7
2. 4
3. 6

Q.

The events which, when put together, consist of all the possible outcomes in an experiment, are called

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Q.

What is the probability that a leap year selected at random will consist of $53$ Sundays?

Q. The probability of flipping a fair coin and getting tail is?

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

Q. Find the next one term of the following sequence: $4,7,10,13,.....$

Q.

A class contains 12 boys and 8 girls. The teacher calls on a student at random to go to the chalkboard. What is the probability that the first person called is a boy? Give the answer up to 1 decimal place.

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Q. Oliver rolls a $6$-sided die once. What will be the probability that he will get an even number?

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