Theoretical Probability

Q.

There Are Two Bags $A$ and $B$. $A$Contains $6RedFlowers$ and $3PinkFlowers$. Where As Bag $B$ Contains$2RedFlowers$ and $7PinkFlowers$. One Flower Is Chosen From a Bag Randomly. What Is the Probability That the Flower Chosen Is $Pink$?

Q.

Two coins are tossed simultaneously. The probability of getting at least one head is __.

Q.

One card is drawn at random from a pack of $52$ cards. What is the probability that the card drawn is a face card?

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

2. $\frac{2}{13}$

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

4. $\frac{5}{26}$

Q.

Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 3 or 5?

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

2. $\frac{3}{20}$
3. $\frac{9}{20}$

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

Q.

What is the probability of not picking a face card when you draw a card at random from a pack of 52 cards?

1. $\frac{1}{13}$

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

3. $\frac{10}{13}$

4. $\frac{12}{13}$

Q.

Whats the difference between biased and unbiased Die?

Q.

A coin is tossed and a dice is rolled. The probability that the coin shows the head and the dice shows 6 is.

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

2. $\frac{1}{12}$

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

4. $1$

Q.

In a game two players $A$ and $B$ take turns in throwing a pair of fair dice starting with player $A$ and the total of scores on the two dice, in each throw is noted.

$A$ wins the game if he throws a total of $6$ before $B$ throws a total of $7$ and $B$ wins the game if he throws a total of $7$ before A throws a total of six

The game stops as soon as either of the players wins.

The probability of $A$ winning the game is :

1. $\frac{5}{31}$

2. $\frac{31}{61}$

3. $\frac{30}{61}$

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

Q. The final marks in mathematics of 30 students are as follows:
53, 61, 48, 60, 78, 68, 55, 100, 67, 90
75, 88, 77, 37, 84, 58, 60, 48, 62, 56
44, 58, 52, 64, 98, 59, 70, 39, 50, 60

(i) Arrange these marks in the ascending order, 30 to 39 one group, 40 to 49 second group, etc.
Now answer the following:

(ii) What is the highest score?

(iii) What is the lowest score?

(iv) What is the range?

(v) If 40 is the pass mark how many have failed?

(vi) How many have scored 75 or more?

(vii) Which observations between 50 and 60 have not actually appeared?

(viii) How many have scored less than 50?

Q. What will be the probability that two friends have the same birthday date in a normal year ?

1. $\frac{1}{73}$
2. $\frac{1}{365}$
3. $\frac{7}{365}$
4. $\frac{12}{365}$

Q.

The probability that a man will be alive in $20$years is $\frac{3}{5}$ and the probability that his wife will be alive in $20$years is $\frac{2}{3}$. Then the probability that at least one will be alive in $20$years is

1. $\frac{13}{15}$

2. $\frac{7}{15}$

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

4. None of these

Q.

There are $2$ bags A and B. Bag A contain $6$ red flowers and $3$ pink flowers where as bag B contains $2$ red flowers and $7$ pink flowers. One flower is chosen from the bag randomly. What is the probability that the flower chosen is pink?

Q.

One hundred identical coins each with a probability $p$ of showing up heads are tossed once. If $0<p<1$ and the probability of heads showing on $50$ coins are equal to that of heads showing on $51$ coins, then the value of $p$ is

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

2. $\frac{49}{101}$

3. $\frac{50}{101}$

4. $\frac{51}{101}$

Q.

Box A contains 25 slips of which 19 marked Rs 1 and other are marked Rs 5 each. Box B contains 50 slips of which 45 marked Rs 1 each and others are marked Rs 13 each. Slips of both boxes are poured into a third box and reshuffled. A slip is drawn at random. What is the probability that it is marked other than Rs 1?

Q.

The probability of drawing a spade or a 3 from a well-shuffled deck of 52 cards is $\frac{17}{52}$.

1. True

2. False

Q.

A bag contains $4$ white balls, $5$ red balls, $8$ black balls, and $3$ blue balls. A ball is drawn at random from the bag. Find the probability that the ball drawn is white, red or blue, not black, and neither black nor red

Q.

A box contains $5$ red marbles, $8$ white marbles and $4$ green marbles. One marble is taken out of the box at random. What is the probability that the marble taken out will be (i) red? (ii) white? (iii) not green?

Q. A letter is chosen from English alphabet. Find the probability of the letter being a vowel.

1. $\frac{3}{26}$
2. $\frac{1}{2}$
3. $\frac{5}{26}$
4. $\frac{8}{26}$

Q. Two coins are tossed simultaneously for 360 times. The number of times ‘2 Tails’ appeared was three times the number ‘No Tail’ appeared and the number of times ‘1 tail’ appeared is double the number of times ‘No Tail’ appeared. What is the probability of getting ‘Two tails’?

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

Q.

If the sum of probabilities of two events is 1, then they are ___________.

1. supplementary
2. complementary
3. equal
4. none of the above

Q.

Any subset of an event is called sample space.

1. True

2. False

Q. An experiment is a method that can be repeated infinitely and has a well-defined set of possible outcomes.

1. True
2. False

Q.

A bag contains $3$ white and $5$ black balls, One ball is drawn at random. Then, the probability that it is white is,

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

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

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

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

Q.

If 20 students in a class failed an exam, the probability of a student selected at random getting passed in an exam is 0.6. The number of students in the class is = ___ .

Q. Question 21 (ii)
A lot consists of 144 ball pens of which 20 are defective and the others are good. Nuri will buy a pen if it is good, but will not buy if it is defective. The shopkeeper draws one pen at random and gives it to her. What is the probability that she will not buy it?

Q. The score of the students are given below. How many students scored between 30 to 50?

1. 50
2. 24
3. 16
4. Cannot be determined

Q.

What is the mathematical study of chance called?

__

Q.

A coin is tossed 500 times and we get

heads : 285 times and tails : 215 times. When a coin is tossed at random, what is the probability of getting

(i) a head? (ii) a tail?

Q.

When a coin is tossed, what is the probability of occurrence of "head" as the outcome?

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

Q.

Experimental probability is also known as?

__