Calculating Probability of an Event

Q.

A card is drawn at random from a pack of 52 cards. Find the probability that the card drawn is :

(i) a black king

(ii) either a black card or a king

(iii) black and a king

(iv) a jack, queen or a king

(v) neither a heart nor a king

(vi) spade or an ace

(vii) neither a red card nor a queen

(ix) other than an ace

(x) a ten

(xi) a spade

(xii) a black card

(xiii) the seven of clubs

(xiv) jack

(xv) the ace of spades

(xvi) a queen

(xvii) a heart

(xviii) a red card

Q.

One card is drawn at random from a well-shuffleed deck of 52 cards. Find the probability that the card drawn is (i) a 4 (ii) a queen (iii) a black card.

Q.

In a deck of 52 cards, there are 4 kings, 4 queens, 4 jacks . These are known as face cards. If one card from the deck is withdrawn, what is the probability that it is not a face card?

1. 

2. 

3. 

4. 

Q.

A letter is chosen from the word 'MATHEMATICS'. What is the probability that the chosen letter is a vowel?

1. $\frac{4}{10}$

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

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

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

Q.

If in a lottery there are $5$ prizes and $20$ blanks, then the probability of getting a prize is

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

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

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

4. None of these

Q.

Find the probability of getting a number less than 5 when a die is thrown.

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

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

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

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

Q.

If a coin is tossed 3 times, what is the probability of getting no head?

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

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

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

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

Q.

From a pack of 52 cards the probability of getting a card of heart when a card is picked at random is___.

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

Q. Two coins are tossed together. Find the probability of getting:
(i) exactly one tail
(ii) at least one head
(iii) no head
(iv) at most one head

Q. Two dice are thrown at the same time. Find the probability that the sum of the two numbers appearing on the top of the dice is:
(i) 0
(ii) 12
(iii) less than 12
(iv) less than or equal to 12

Q.

A dice is rolled twice. Find the probability that $5$ will not come up either time.

Q.

The probability that it will rain tommmorow is 0.85. What is the probability that it will not rain tommorow ?

Q.

A bag contains 3 red balls, 5 black balls and 4 white balls. A ball is drawn at random from the bag. What is the probability that the ball drawn is :

(i) white ? (ii) red ? (iii) black ? (iv) not red ?

Q.

A bag contains $4$ red, $5$ black and $6$ white balls. A ball is drawn from the bag at random. Find the probability that the ball drawn is:

(i) white (ii) red (iii) not black (iv) red or white

Q.

If a coin is tossed 2 times, what is the probability of getting at least one tail?

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

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

3. $1$

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

Q.

It is known that a box of 100 electric bulbs contains 8 defeective bulbs. One bulb is taken out at random from the box. What is the probability that the bulb drawn is (i) defective ? (ii) non-defective?

Q.

A bag contains 5 white and 7 red balls. One ball is drawn at random. What is the probability that ball drawn is white?

Q.

The probability of getting a composite number in a throw of dice is

1. 1/2

2. 1/6

3. 1

4. 1/3

Q.

$5$ boys and $5$ girls are sitting in a row randomly. The probability that boys and girls sit alternatively is

1. $\frac{5}{126}$

2. $\frac{1}{42}$

3. $\frac{4}{126}$

4. $\frac{1}{126}$

Q.

From past experience, a professor knows that the test score of a student taking her final examination is a random variable with mean $75$.

a. Give an upper bound for the probability that a students test score will exceed $85$.

Suppose, in addition, that the professor knows that the variance of a students test score is equal to equal to $25$.

b. What can be said about the probability that a student will score between $65$ and $85$.

c. How many students would have to take the examination to ensure with probability at least $0.9$ that the class average would be within $5$ of $75$?

Do not use the central limit theorem.

Q.

A coin is tossed twice. Find the probability of getting:
(i) exactly one head
(ii) exactly one tail
(iii) two tails
(iv) two heads

Q. A bag contains 3 white, 5 black and 2 red balls, all of the same shape and size. A ball is drawn from the bag without looking into it, find the probability that the ball drawn is:
(i) a black ball
(ii) a red ball
(iii) a white ball
(iv) not a red ball
(v) not a black ball

Q.

Question 7

In a school, only 3 out of 5 students can participate in a competition. What is the probability of the students who do not make it to the competition?

(a) 0.65

(b) 0.4

(c) 0.45

(d) 0.6

Q.

In a lottery, there are 10 prizes and 20 blanks. A ticket is chosen at random. What is the probability of getting a prize?

Q.

Can the experimental probability of an event be a negative number? If not, why?

Q.

An urn contains 10 red and 8 white balls. One ball is drawn at random. Find the probability that the ball drawin is white.

Q.

Question 77

The probability of getting number 6 in a throw of a die is $\frac{1}{6}.$ Similarly, the probability of getting a number 5 is $\frac{1}{5}.$

Q.

You have an eight-faced die. In this die, one of the faces contains 1, two faces contain 2, three faces contain 3 and other faces contain a 4 and a 5 respectively. What is the probability of getting a 3 when the die is rolled? (All outcomes are equally likely).

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

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

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

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

Q. From 10 identical cards, numbered 1, 2, 3, ......, 10, one card is drawn at random. Find the probability that the number on the card drawn is a multiple of:
(i) 2
(ii) 3
(iii) 2 and 3
(iv) 2 or 3

Q.

For an multiple choice question the number of options given are 4. Find the probability of doing the question wrong.

1. 1

2. 0

3. 3/4

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