Theoretical Probability

Q.

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

1. 
2. 
3. 
4. 

Q. A fish tank has $5$ male fish and $8$ female fish. What is the probability of fish taken out is a male fish?

1. $\frac{5}{8}$
2. $\frac{8}{13}$
3. $\frac{5}{13}$
4. $\frac{8}{5}$

Q. What is the probability of rolling a fair die getting a number less than or equal to $6$?

1. $P(Number\le 6)=\frac{1}{6}$
2. $P(Number\le 6)=\frac{1}{2}$
3. $P(Number\le 6)=1$
4. None of the above

Q. The probability that a non leap year selected at random will contain $53$ Sundays is

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

Q.
Given that the above spinner is fair, what is the probability that the spinner stops at $Green$?

1. $P\left(Green\right)=\frac{1}{4}$
2. $P\left(Green\right)=\frac{1}{5}$
3. $P\left(Green\right)=\frac{1}{6}$
4. None of the above

Q. A coin is tossed 240 times and head obtained 160 times. Now, if a coin is tossed at random, what is the probability of getting a tail?

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

Q. Grades of 20 students is given below. The probability of getting grade "B" is

1. 33.33%
2. 30%
3. 40%

Q. When a single dice is rolled, what is the probability of getting a prime number?

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

Q. The time spent for various activites are given in the form of a pie chart below. Predict the total time spent for walking if totally 45 hours are spent for all the activities in a week.

1. 10 hours
2. 6 hours
3. 15 hours
4. 20 hours

Q. A coin is tossed 1000 times with the following frequencies:
Head: 445, Tail: 555
When a coin is tossed at random, what is the probability of getting it?
(i) A head?
(ii) A tail?

Q. A coin is tossed 240 times and head obtained 160 times. Now, if a coin is tossed at random, what is the probability of getting a tail?

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

Q.

In the game of ludo, you start your move if you get 6 after throwing the dice for the first time. What is the probability that you will start your move after the first throw?

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

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

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

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

Q. What is the probability of rolling a fair die and getting a number greater than 2?

1. $P(Num>2)=\frac{1}{3}$
2. $P(Num>2)=\frac{2}{3}$
3. $P(Num>2)=\frac{1}{6}$
4. $P(Num>2)=\frac{5}{6}$

Q. A survey about 150 movies is shown as:

For the given data, if the probability of randomly selecting a movie that is a combo of action movies and cartoon movies is $\frac{A}{5}$, find the value of A.

1. 2

Q. An experiment consists of rolling a fair die. Find the theoretical probability of rolling a number greater than $5.$

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

Q.
Students in a class each write down on a piece of paper a letter of their choice and fold it and put it into a bowl. Given above are those letters. Alex picks a piece of paper at random from the bowl. What is the probability that Alex picks a paper with;

1. The first letter of his name written on it?
2. With an S on it?

1. $P\left(\text{Alex picking an A}\right)=\frac{1}{17}$
   $P\left(\text{Alex picking a S}\right)=\frac{1}{17}$
2. $P\left(\text{Alex picking an A}\right)=\frac{1}{17}$
   $P\left(\text{Alex picking a S}\right)=\frac{4}{17}$
3. $P\left(\text{Alex picking an A}\right)=\frac{4}{17}$
   $P\left(\text{Alex picking a S}\right)=\frac{1}{17}$
4. $P\left(\text{Alex picking an A}\right)=\frac{4}{17}$
   $P\left(\text{Alex picking a S}\right)=\frac{4}{17}$

Q. Theoretical probability can be written as which of the following?

1. $\frac{\text{Favorable outcomes}}{\text{Total unfavorable outcomes}}$
2. $\frac{\text{Favorable outcomes}}{\text{Total favorable outcomes}}$
3. $\frac{\text{Total favorable outcomes}}{\text{Favorable outcomes}}$
4. None of the above

Q. A batsman hits boundaries for $5$ times out of $25$ balls. Find the probability that he did not hit the boundaries.

1. $\frac{2}{5}$
2. $\frac{3}{5}$
3. $\frac{4}{5}$
4. None of the above

Q. How many numbers between 400 and 600 begin with or end with a digit of a 5?

1. 40
2. 100
3. 110
4. 120

Q.

If three different coins are tossed together, what is the probability of getting two heads?

Q.
Given that the avobe spinner is fair, what is the probability of getting a blue, green or red?

1. $P(Blue,Green,Red)=\frac{1}{6}$
2. $P(Blue,Green,Red)=\frac{2}{5}$
3. $P(Blue,Green,Red)=\frac{1}{2}$
4. None of the above

Q. When we pick a fruit from the basket, the total number of possible outcomes is .

1. 2
2. 1
3. 3

Q. The theoretical probability of getting a heads if we toss a fair die is ?

1. $\frac{1}{3}$
2. $\frac{1}{2}$
3. $\frac{1}{4}$
4. Cannot be Determined

Q.

The probability of getting at least one tail in 4 throws of a coin is

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

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

3. $\frac{15}{16}$

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

Q. To pick a lab partner, each student must write his/her name down on a piece of paper and drop it into a bowl. Students would then pick the pieces of paper from that bowl to get their lab partners. Given that Kevin was the first one to pick a chit and he has 5 friends in his class and there are 20 students in the class, what is the probability that Kevin's partner will be one of his friends?

1. $P\left(\text{lab partner is Kevin's friend}\right)=0\%$
2. $P\left(\text{lab partner is Kevin's friend}\right)=25\%$
3. $P\left(\text{lab partner is Kevin's friend}\right)=50\%$
4. $P\left(\text{lab partner is Kevin's friend}\right)=75\%$

Q. Hussain has $5red$, $3blue$ and $2green$ socks. If a sock is drawn at random, what is the probability that the sock is:

1. Red
2. Blue
3. Green

1. $P\left(Red\right)=\frac{1}{2}$
   $P\left(Blue\right)=\frac{1}{10}$
   $P\left(Green\right)=\frac{1}{5}$
2. $P\left(Red\right)=\frac{1}{2}$
   $P\left(Blue\right)=\frac{1}{5}$
   $P\left(Green\right)=\frac{1}{10}$
3. $P\left(Red\right)=\frac{1}{2}$
   $P\left(Blue\right)=\frac{3}{10}$
   $P\left(Green\right)=\frac{1}{5}$

Q. There are 121 articles in a bag. Out of which 11 are defective articles. If you just pick one article at random,
(i) what is the probability of picking the non-defective article?
(ii) If the article drawn the first time is non-defective and is not replaced, then find the probability of getting the defective article in the next draw.

Q. 48 ice-creams are placed on a table. Some are chocolate flavoured and others are vanilla flavoured. If a person takes an ice-cream at random from the table, the probability that it is chocolate flavoured is $\frac{2}{3}$. Find the number of vanilla flavoured ice-creams on the table.

Q. The probability do raining on Tuesday is 0.3 and that on Wednesday is 0.2. What is the probability of raining on both the days.

Q. Five cards - the ten, jack, queen , king and ace of diamonds are well-shuffled with their face downwards. One card is then picked up at random.
$\left(i\right)$ What is the probability that the card is jack?
$\left(ii\right)$ If the king is drawn and put aside, what is the probability that the second card picked up is $\left(a\right)$a queen and $\left(b\right)$a ten?

1. $\left(i\right)\frac{1}{7}\left(ii\right)\left(a\right)\frac{1}{6},\left(b\right)\frac{1}{2}$
2. $\left(i\right)\frac{1}{5}\left(ii\right)\left(a\right)\frac{1}{4},\left(b\right)\frac{1}{4}$
3. $\left(i\right)\frac{1}{6}\left(ii\right)\left(a\right)\frac{1}{6},\left(b\right)\frac{1}{3}$
4. $\left(i\right)\frac{1}{4}\left(ii\right)\left(a\right)\frac{1}{4},\left(b\right)\frac{1}{3}$