Event and Outcome

Q.

What is the difference between at least one head and at most one head in probability?

Q. A number is selected at random from the numbers 3, 5, 5, 7, 7, 7, 9, 9, 9, 9 The probability that the selected number is their average is

(a) $\frac{1}{10}$

(b) $\frac{3}{10}$

(c) $\frac{7}{10}$

(d) $\frac{9}{10}$

Q. A girl calculates that the probability of her winning first prize in a lottery is 0.08. If 6000 tickets are sold, then how many tickets has she bought?

1. 480
2. 40
3. 240
4. 740

Q.

The probability that a non-leap year selected at random will have 53 Mondays is

1. ⁴⁵/₅₂

2. ⁷/₅₂

3. ¹/₇

4. ⁵²/₃₆₅

Q.

If three dice are thrown together, then the probability of getting $5$ on at least one of them is

1. $\frac{125}{216}$

2. $\frac{215}{216}$

3. $\frac{1}{216}$

4. $\frac{91}{216}$

Q.

The probability of the product of a perfect square when$2$dice are thrown together, is:

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

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

3. $\frac{5}{18}$

4. None of these

Q.

A coin is tossed two times. Find the probability of getting at most one head.

1. 0.55

2. 0.75

3. 0.65

4. 0.25

Q.

An integer is chosen at random between 1 to 100 .find the probability that it is:(i) divisible by 8 (i)not divisible by 8.

Q. Question 23
A girl calculates that the probability of her winning the first prize in a lottery is 0.08. If 6000 tickets are sold, then how many tickets has she bought?
(a) 40
(b) 240
(c) 480
(d) 750

Q. Question 22
Two dice are thrown at the same time and the product of numbers appearing on them is noted. Find the probability that the product is less than 9.

Q. A number x is selected at random from the numbers 1, 4, 9, 16 and another number y is selected at random from the numbers 1, 2, 3, 4. Find the probability that the value of xy is more than 16.

Q.

If two coins are tossed $5$ times, then the probability of getting $5$ heads and $5$ tails is

1. $\frac{63}{256}$

2. $\frac{1}{1024}$

3. $\frac{2}{205}$

4. $\frac{9}{64}$

Q.

A number x is chosen from the numbers -3, -2, -1, 0, 1, 2, 3. The probability that |x|< 2 is

1. ⁵/₇

2. ²/₇

3. ³/₇

4. ¹/₇

Q. A number is selected from numbers 1 to 25. The probability that it is prime is

(a) $\frac{2}{3}$

(b) $\frac{1}{6}$

(c) $\frac{1}{3}$

(d) $\frac{5}{6}$

Q.

Three different dice are thrown three times. What is the probability that they show different numbers only two times?

Q.

Two dice are tossed. The probability that the total score is a prime number is

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

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

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

4. None of these

Q.

What is the probability of getting a “FULL HOUSE” in five cards drawn in a poker game from a standard pack of $52$-cards?

[A FULL HOUSE consists of $3$ cards of the same kind (eg, $3$ Kings) and $2$ cards of another kind (eg, $2$ Aces)]

1. $\frac{6}{4165}$

2. $\frac{4}{4165}$

3. $\frac{3}{4165}$

4. None of these

Q. A card is selected at random from a deck of 52 playing cards. The probability of not getting a face card is

1. 
   $\frac{12}{13}$
2. 
   $\frac{10}{13}$
3. 
   $\frac{11}{52}$
4. 
   $\frac{3}{13}$

Q.

A game of chance consists of spinning an arrow which comes to rest pointing at one of the numbers 1, 2, 3, 4, 5, 6, 7, 8 (see the given figure), and these are equally likely outcomes. What is the probability that it will point at

(i) 8?

(ii) an odd number?

(iii) a number greater than 2?

(iv) a number less than 9?

Q.

Which of the following arguments are correct and which are not correct? Give reasons for your answer.

(i) If two coins are tossed simultaneously there are three possible outcomes−−two heads, two tails or one of each. Therefore, for each of these outcomes, the probability is.

(ii) If a die is thrown, there are two possible outcomes−−an odd number or an even number. Therefore, the probability of getting an odd number is.

Q. A number x is selected at random from the numbers 1, 2, 3 and 4. Another number y is selected at random from the numbers 1, 4, 9 and 16. Find the probability that product of x and y is less than 16.

Q.

Find the probability of getting a multiple of 2 on one die and a multiple of 3 on the other die, if pair of dice are thrown.

1. 
   $\frac{5}{18}$
2. 
   $\frac{1}{4}$
3. 
   $\frac{1}{3}$
4. 
   $\frac{11}{36}$

Q.

A coin is tossed once. What is the probability of getting tail?

Q. Find the probability that a number selected at random from the numbers 1, 2, 3, ..., 35 is a
(i) prime number

(ii) multiple of 7

(iii) a multiple of 3 or 5

Q. If a number 'x' is chosen from the nos. 1, 2, 3 and number 'y' is selected from the numbers 1, 4, 9.
Find the probability that xy=10

Q.

What is the probability that a positive integer not exceeding $100$ selected at random is divisible by $3$$?$

Q.

The corners of regular tetrahedrons are numbers $1,2,3,4$. Three tetrahedrons are tossed. The probability that the sum of upward corners will be $5$ is

1. $\frac{5}{24}$

2. $\frac{5}{64}$

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

4. $\frac{3}{16}$

Q.

A die is rolled. If $\mathrm{X}$ denotes the number of positive divisors of the outcomes then the range of the random variable $\mathrm{X}$ is

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

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

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

4. $\{1,3,5\}$

Q. Four unbiased coins are tossed simultaneously. The probability that exactly two heads occur will be

1. 
   $\frac{1}{16}$
2. 
   $\frac{3}{8}$
3. 
   $\frac{3}{16}$
4. 
   $\frac{5}{16}$

Q.

A standard pair of six-sided dice are rolled. What is the probability of rolling a sum less than or equal to $10$ ?