Classical definition of probability

Q.

A random variable $X$ takes values $0,1,2,3,...$ with probability $P(X=x)=k(x+1){\left(\frac{1}{5}\right)}^x$, where $k$ is a constant, then $P(X=0)$ is equal to

1. $\frac{7}{25}$

2. $\frac{18}{25}$

3. $\frac{13}{25}$

4. $\frac{19}{25}$

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

Q.

A four-digit number is formed by the digits $1,2,3,4$ with no repetition.

The probability that the number is odd is

1. Zero

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

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

4. None of these

Q.

If an integer $q$ be chosen at random in the interval $-10\le q\le 10$ then the probability that the roots of the equation $x^2+qx+(3/4)q+1=0$ are real is

Q.

If the odds in favour of an event be $3:5$, then the probability of non-occurrence of the event is

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

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

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

4. $\frac{5}{8}$

Q. If an unbiased coin is tossed and two fair dice are rolled at the same time, then what is the probability that head is the outcome and sum of the numbers on the dice is 9?

1. $\frac{1}{2}$
2. $\frac{1}{9}$
3. $\frac{1}{18}$
4. $\frac{1}{36}$

Q. Let `head` means 1 and `tail` means 2 and coefficients of the equation $a{x}^2+bx+c=0$ are chosen by tossing a fair coin. The probability that the roots of the equation are non-real, is equal to

1. $\frac{5}{8}$
2. $\frac{7}{8}$
3. $\frac{3}{8}$
4. $\frac{1}{8}$

Q. A fair die is thrown until a score of less than five points is obtained. The probability of obtaining less than three points on the last throw is

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

Q.

An experiment consists of tossing a coin and rolling a die.
(a) Find the sample space.
(b) Find the probability of getting heads and an even number.
(c) Find the probability of getting heads and a number greater than.$4.$
(d) Find the probability of getting tails and an odd number.

Q. A five digit number is formed with digits 0. 1. 2. 3. 4 without repetition. A number is selected at random, then the probability that it is divisible by 4 is

1. $\frac{1}{3}$
2. $\frac{5}{16}$
3. $\frac{1}{4}$
4. $\frac{4}{15}$

Q. A four digit number (numbered from 0000 to 9999) is said to be lucky if sum of its first two digits is equal to the sum of its last two digits. If a four digit number is picked up at random, then the probability that it is a lucky number is:

1. 0.07
2. 0.67
3. 0.067
4. None

Q. A number of five digits is formed with the digits 0, 1, 2, 3, 4 without repetition. The probability that it is a number divisible by 4 is:

1. $\frac{5}{16}$
2. $\frac{1}{4}$
3. $\frac{4}{15}$
4. $\frac{1}{3}$

Q. A card is drawn at random from a pack of 100 cards numbered 1 to 100. The probability of drawing a number, which is a square, is:

1. $\frac{2}{5}$
2. $\frac{1}{5}$
3. $\frac{1}{10}$
4. $None$

Q. Cards numbered $1$ to $30$ are put in a bag. A card is drawn at random from the bag. Find the probability that the number on the drawn card is not a perfect square number.

Q. Five different objects 1, 2, 3, 4, 5 are distributed randomly in 5 places marked 1, 2, 3, 4, 5. One arrangement is picked at random. The probability that in the selected arrangement, none of the object occupies the place corresponding to its number is:

1. $\frac{119}{120}$
2. $\frac{11}{30}$
3. $None$
4. $\frac{1}{5}$

Q. Two persons each makes a single throw with a pair of dice. Then the probability that the sum on both dice are unequal, is:

1. $\frac{73}{648}$
2. $\frac{575}{648}$
3. $None$
4. $\frac{57}{648}$

Q. Two numbers b and c are chosen at random (with replacement from the numbers 1, 2, 3, 4, 5, 6, 7, 8 and 9). The probability that $x^2+bx+c>0$ for all $x\in R$ is

1. $\frac{45}{143}$
2. $\frac{32}{81}$
3. $\frac{82}{125}$
4. $\frac{17}{123}$

Q. From a bag containing 10 distinct balls, 6 balls are drawn simultaneously and replaced. Then 4 balls are drawn. The probability that exactly 3 balls are common to the drawings is

1. $\frac{8}{21}$
2. $\frac{5}{24}$
3. $\frac{9}{22}$
4. $\frac{6}{19}$

Q. The probability that out of 10 persons, all born in April, at least two have the same birthday is

1. $\frac{{}^{30}{P}_{10}}{(30{)}^{10}}$
2. $1-\frac{{}^{30}{P}_{10}}{30!}$
3. $\frac{{30}^{10}{-}^{30}{P}_{10}}{{30}^{10}}$
4. $noneofthese$

Q. Assume that a bag contains 4 red squares, 3 red rectangles, 5 blue squares and 4 blue circles. An object is taken out from the bag. What is the probability of taking out a blue square?

1. $\frac{5}{15}$
2. $\frac{4}{16}$
3. $\frac{5}{16}$
4. $\frac{6}{16}$