Notion of chance or probability

Q. Two dice are thrown simultaneously. What is the probability of getting two numbers whose product is even?

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

Q.

Probability of occurrence of an event is defined as

1. Number of trials in which the event not happened divided by the total number of trials.

2. The total number of trials divided by Number of trials in which the event happened

3. The total number of trials multiplied by Number of trials in which the event happened

4. Number of trials in which the event happened divided by the total number of trials.

Q.

There are 500 tickets of a lottery out of which 10 are prize winning tickets. A person buys one ticket. Find the probability that he gets a prize winning ticket.

1. $\frac{1}{10}$

2. $\frac{1}{100}$

3. $\frac{1}{50}$

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

Q.

Randomly two balls are drawn from a bag containing 3 green balls and 5 red balls. What is the probability that the balls drawn contain at least one red ball (without replacement)?

1. $\frac{25}{28}$

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

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

4. $\frac{5}{28}$

Q.

A number is chosen at random from the first ten natural numbers. The probability that number is odd and perfect square is

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

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

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

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

Q.

If you flip a coin and roll a $6$-sided die, what is the probability that you will flip a head and roll an even number?

Q.

Numbers $1$ to $10$ are written on ten separate slips (Each number on different slip) , kept in a box and mixed well. One slip is chosen from the box without looking into it. What is the probability of getting a one-digit number ?

Q.

If we roll a die, there are total six possible outcomes (1, 2, 3, 4, 5, 6). What is the probability of getting 2?

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

Q.

There is a five-volume dictionary among $50$ books arranged on a shelf in random order. If the volumes are not necessarily kept side by side, the probability that they occur in increasing order from left to right is

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

2. $\frac{1}{5^{50}}$

3. $\frac{1}{{50}^5}$

4. None of these

Q.

If a coin is tossed three times, then what is the probability that at least one head occurs in the three trials?

1. $\frac{7}{8}$

2. $\frac{5}{6}$

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

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

Q.

If a number $n$ is chosen at random from the set $\left\{11,12,13,.........,30\right\}$. Then, the probability that $n$ is neither divisible by $3$ nor divisible by $5$, is

1. $\frac{7}{20}$

2. $\frac{9}{20}$

3. $\frac{11}{20}$

4. $\frac{13}{20}$

Q. In a cricket match, a batsman hits a boundary 5 times every 30 balls he plays. Find the probability that he did not hit a boundary.

1. 
2. 
3. 
4. 

Q.

A die is thrown 1000 times with the frequencies for the outcomes 1, 2, 3, 4, 5 and 6 as given in the following table:

$$\begin{array}{cc}Outcome& Frequency\\ 1& 165\\ 2& 175\\ 3& 180\\ 4& 150\\ 5& 145\\ 6& 185\end{array}$$

What is the probability of getting a 2 or a 4?

1. 0.325

2. 0.515

3. 0.455

4. 0.245

Q. In a school of 1900 students, there are 800 girls. Find the probability that a student chosen at random is a boy.

1. $\frac{11}{27}$
2. $\frac{8}{19}$
3. $\frac{11}{8}$
4. $\frac{11}{19}$

Q.

What is the probability of drawing the black slice of the pizza? [2 MARKS]

Q.

$\begin{array}{cccccccccccccccc}\text{Bus}& 1& 2& 3& 4& 5& 6& 7& 8& 9& 10& 11& 12& 13& 14& 15\\ \text{Arrival time(hr:min)}& 8:15& 8:18& 8:23& 8:29& 8:32& 8:40& 8:45& 8:52& 8:54& 9:00& 9:07& 9:13& 9:20& 9:25& 9:32\end{array}$

In the above observation, how many buses have arrived within 5 minutes of the bus just before them?

1. 4

2. 7

3. 5

4. 8

Q.

It is 82% likely that India will win the match means that, ___.

1. there is 100% chance that India will win.

2. there is 18% chance for India to lose the match. So India will definitely not win.

3. there is 82% chance that India will win. So India will certainly win.

4. there is 82% chance that India will win but we cannot say that India will definitely win.

Q. Cards marked with numbers 40 , 41 , 42..........60 are well shuffled and a card is drawn at random. What is the probability that the number on the card is a perfect square?

1. $\frac{1}{21}$
2. $\frac{4}{20}$
3. $\frac{1}{19}$
4. $\frac{5}{19}$

Q.

If two dice are thrown simultaneously, then the probability that the sum of the numbers which come up on the dice to be more than $5$ is.

1. $\frac{5}{36}$

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

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

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

5. none of these

Q.

Three coins are tossed once. Find the probability of getting all tails.

Q.

A die is thrown 1000 times with the frequencies for the outcomes 1, 2, 3, 4, 5 and 6 as given in the following table:

$$\begin{array}{ccccccc}Outcome& 1& 2& 3& 4& 5& 6\\ Frequency& 165& 175& 180& 150& 145& 185\end{array}$$

What is the probability of getting a 2 or a 4?

1. 0.515

2. 0.245

3. 0.325

4. 0.455

Q.

In a village, out of 60 couples, 15 couples were married at the age of 21 to 23, 25 couples were married at the age of 24 to 27 and 16 couples were married at the age of 28 to 30. The rest, after the age of 30. What is the probability that a couple gets married after the age of 30?

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

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

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

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

Q.

$\begin{array}{ccccc}Outcome& 2& 3& 5& 6\\ Frequency& 10& 14& 16& 20\end{array}$

A die was thrown 80 times and the frequency of occurrence of 2, 3, 5 and 6 is given in the table. What is the probability of occurrence of 1 or 4?

1. 1

2. 0.67

3. 0.25

4. 0

Q.

Three coins are tossed simultaneously 200 times with the following frequencies of different outcomes.

$$\begin{array}{ccccc}Outcomes& 3heads& 2heads& 1head& Nohead\\ Frequency& 23& 72& 77& 28\end{array}$$

Compute the probability of 2 heads coming up.

1. $\frac{9}{25}$

2. $\frac{25}{29}$

3. $\frac{23}{35}$

4. $\frac{7}{11}$

Q. Arrange the events in the increasing order (from top to bottom) of their probabilities, when a die is rolled.

1. Getting 8
2. Even prime no.
3. A multiple of 3
4. A multiple of 2
5. No. less than 6

Q.

5 defective glasses are accidentally mixed with 20 good ones. The good glasses and the defective ones look the same from the outside. If a glass is chosen at random, what is the probability that the chosen glass is good?

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

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

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

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

Q.

A goldsmith can choose between 3 metals A, B or C to make an artefact. What is the probability that he chooses C?

1. 2/3

2. 0

3. 1

4. 1/3

Q. Probability of a sure event is 1.

1. True
2. False

Q.

A survey of $200$ people was conducted about their preference of visiting various pavilions.

Pavilion	Good living	Delhi Pavilion	Toy Pavilion	Defence Pavilion
No. of person	$95$	$45$	$40$	$20$

Find the probability that a person selected at random visited for only Toy pavilion.

Q. The probability of getting a multiple of 2 when an unbiased die is thrown is $\frac{1}{2}$.

1. True
2. False