Classical Definition of Probability

Q.

A software engineer creates a LAN game where an $8$ digit code made up of $1,2,3,4,5,6,7,8$ has to be decided on universal code. There is a condition that each number has to be used and no number can be repeated. What is the probability that first $4$ digits of the code are even numbers ?

Q.

The probability that a leap year will have $53$ Fridays or $53$ Saturdays is

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

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

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

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

Q.

Two dice are thrown together. Then, the probability that the sum of numbers appearing on them is a prime number, is

1. $\frac{5}{12}$

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

3. $\frac{13}{36}$

4. $\frac{11}{36}$

Q.

In a simultaneous throw of a pair of dice, find the probability &getting :

(i) 8 as the sum

(ii) a doublet

(iii) a doublet of prime numbers

(iv) a doublet of odd numbers

(v) a sum greater than 9

(vi) an even number on first

(vii) an even number on one and a multiple of 3 on the other

(vii) neither 9 nor 11 as the sum of thenuntbers on the faces

(ix) a sum less than 6

(x) a sum less than 7

(xi) a sum more than 7

(xii) neither a doublet nor a total of 10

(xiii) odd number on the first and 6 on the second

(xiv) a number greater than 4 on each dice

(xv) a total of 9 or 11

(xvi) a total greater than 8.

Q.

How do you evaluate ${}^{8}C_2$ ?

Q.

A bag contains $8$ red and $7$ black balls. Two balls are drawn at random. The probability that both the balls are of the same colour is

1. $\frac{14}{15}$

2. $\frac{11}{15}$

3. $\frac{7}{15}$

4. $\frac{4}{15}$

Q.

The probability that a randomly chosen $5$digit number is made from exactly two digits is

1. $\frac{134}{{10}^4}$

2. $\frac{121}{{10}^4}$

3. $\frac{135}{{10}^4}$

4. $\frac{50}{{10}^4}$

Q.

The probability of getting a total of atleast $6$ in the simultaneously throw of three dice is

1. $\frac{6}{108}$

2. $\frac{5}{27}$

3. $\frac{1}{24}$

4. $\frac{103}{108}$

Q. A natural number is chosen at random from the first 100 natural numbers. Then the probability, for the in-equation $x+\frac{100}{x}>50$ satisfied, is

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

Q.

In a single throw of two dice, find the probability of getting a total of $10$, getting a total of $9$ or $11$, getting a sum greater than $9$, getting a doublet of even numbers and not getting the same number on the two dice.

Q.

Three dice are thrown simultaneously. What is the probability of getting 15 as the sum ?

Q.

A five digit number is formed using the digits $0,1,2,3,4$ and $5$ without repetition. The probability that number is divisible by $6$?

1. $10\%$

2. $18\%$

3. $20\%$

4. $25\%$

Q.

A man is known to speak the truth $3$ out of $4$ times. He throws a die arid report that it is six. The probability that it actually a six is

1. $\frac{3}{8}$

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

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

4. None of these

Q.

A fair coin is tossed repeatedly. If the tail appears on the first four tosses then the probability of the head appearing on the fifth toss equals

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

2. $\frac{1}{32}$

3. $\frac{31}{32}$

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

Q.

Three digit numbers are formed using the digits 0, 2, 4, 6, 8. A number is chosen at random out of these numbers what is the probability that this number has the same digits ?

1. $\frac{1}{16}$

2. $\frac{16}{25}$

3. $\frac{1}{645}$

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

Q.

If a number $n$ is chosen at random from the set $\left\{1,2,3,........,1000\right\}$. Then, the probability that $n$ is a number that leaves remainder $1$, when divided by $7$, is

1. $\frac{71}{500}$

2. $\frac{143}{1000}$

3. $\frac{72}{500}$

4. $\frac{71}{1000}$

Q.

Find the probability of getting $52$ Sundays in a non-leap year.

Q. The rate of increase of bacteria in a certain culture is proportional to the number present. If it double in 5 hours then in 25 hours, its number would be

1. 32 times the original
2. 64 times the original
3. 8 times the original
4. 16 times the original

Q.

The probability of getting a number greater than $2$ in throwing a die is

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

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

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

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

Q. The coefficients $a,b\text{and}c$ of the quadratic equation, $a{x}^2+bx+c=0$ are obtained by throwing a dice three times. The probability that this equation has equal roots is :

1. $\frac{1}{54}$
2. $\frac{1}{72}$
3. $\frac{1}{36}$
4. $\frac{5}{216}$

Q.

Let $A$denote the event that a $6$-digit integer formed by $0,1,2,3,4,5,6$ without repetitions, be divisible by $3$. Then the probability of event $A$ is equal to

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

2. $\frac{9}{56}$

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

4. $\frac{11}{27}$

Q. Let $A$ be a set of all $4-$digit natural numbers whose exactly one digit is $7.$ Then the probability that a randomly chosen element of $A$ leaves remainder $2$ when divided by $5$ is:

1. $\frac{1}{5}$
2. $\frac{2}{9}$
3. $\frac{97}{297}$
4. $\frac{122}{297}$

Q.

Bag I contains 3 red and 4 black balls and bag II contains 4 red and 5 black balls. One ball is transferred from bag I to bag II and then is drawn from bag II. The ball so drawn is found to be red in colour. Find the probability that the transferred ball is black.

Q.

A and B throw a pair of dice. If A throws 9, find B's chance of throwing a higher number.

Q.

Two dice are thrown simultaneously. The probability of obtaining a total score of 5 is

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

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

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

4. none of these

Q.

If three dice are throw simultaneously, then the probability of getting a score of 5 is

1. $\frac{1}{36}$

2. none of these

3. $\frac{5}{216}$

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

Q.

Two fair dice are rolled simultaneously. The probability that $5$ will come up at least once is:

Q.

Out of $40$ consecutive natural numbers, two are chosen at random. Probability that the sum of the two numbers is odd is

1. $\frac{14}{39}$

2. $\frac{20}{39}$

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

4. None of these

Q. Three randomly chosen non-negative integers $x,y$ and $z$ are found to satisfy the equation $x+y+z=10$. Then the probability that $z$ is even, is

1. $\frac{36}{55}$
2. $\frac{6}{11}$
3. $\frac{1}{2}$
4. $\frac{5}{11}$

Q. Fifteen coupons are numbered 1, 2, . . ., 15, respectively. Seven coupons are selected at random one at a time with replacement. The probability that the largest number appearing on a selected coupon is 9, is

1. ${\left(\frac{9}{15}\right)}^7$
2. ${\left(\frac{9}{15}\right)}^7-{\left(\frac{8}{15}\right)}^7$
3. None of these
4. ${\left(\frac{8}{15}\right)}^7$