# Classical Definition of Probability

## Trending Questions

**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

27

37

47

17

**Q.**

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

$\frac{5}{12}$

$\frac{7}{18}$

$\frac{13}{36}$

$\frac{11}{36}$

**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

$\frac{14}{15}$

$\frac{11}{15}$

$\frac{7}{15}$

$\frac{4}{15}$

**Q.**

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

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

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

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

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

**Q.**

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

$\frac{6}{108}$

$\frac{5}{27}$

$\frac{1}{24}$

$\frac{103}{108}$

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

- 120
- 1120
- 13
- 14

**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?

10%

18%

20%

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

$\frac{3}{8}$

$\frac{1}{5}$

$\frac{3}{4}$

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

$\frac{1}{2}$

$\frac{1}{32}$

$\frac{31}{32}$

$\frac{1}{5}$

**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 ?

116

1625

1645

125

**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

$\frac{71}{500}$

$\frac{143}{1000}$

$\frac{72}{500}$

$\frac{71}{1000}$

**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

- 32 times the original
- 64 times the original
- 8 times the original
- 16 times the original

**Q.**

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

$\frac{1}{3}$

$\frac{2}{3}$

$\frac{1}{2}$

$\frac{1}{6}$

**Q.**The coefficients a, b and c of the quadratic equation, ax2+bx+c=0 are obtained by throwing a dice three times. The probability that this equation has equal roots is :

- 154
- 172
- 136
- 5216

**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

$\frac{4}{9}$

$\frac{9}{56}$

$\frac{3}{7}$

$\frac{11}{27}$

**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:

- 15
- 29
- 97297
- 122297

**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

118

112

19

none of these

**Q.**

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

136

none of these

5216

16

**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

$\frac{14}{39}$

$\frac{20}{39}$

$\frac{1}{2}$

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

- 3655
- 611
- 12
- 511

**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

- (915)7
- (915)7−(815)7
- None of these
- (815)7