Probability of an Event "A" to Happen

Q.

If a coin is tossed 3 times, what is the probability of getting atleast one tail?

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

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

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

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

Q. From a pack of 52 playing card, Jacks, Queens and Kings of red colour are removed. From the remaining, a card is drawn at random. Find the probability that drawn card is:

(i) a black King, (ii) a card of red colour, (iii) a card of black colour.

Q. A card is drawn at random from a well-shuffled deck of playing cards. Find the probability that the card drawn is
(i) A card of spade or an ace
(ii) A black king
(iii) Neither a jack nor a king
(iv) Either a king or a queen

Q.

On a dart board of radius 50 cm, what is the probability that you hit the bull's eye of radius 5 cm?

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

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

3. 1

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

Q.

There are 50 mangoes in a basket, 20 of which are unripe. Another basket contains 40 mangoes, with 15 unripe. If we take one mango from each basket, what is the probability of both being ripe?

1. 0

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

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

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

Q.

A coin is tossed three times in succession. If $E$ is the event that there are at least two heads and $F$ is the event in which first throw is a head, then $P\left(E\right|F)=$

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

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

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

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

Q.

If P(E) and P(E’) are the probabilities of two complementary events, then which of the following is always true?

1. $P\left(E\right)+P\left(E^{\prime }\right)=0$

2. $P\left(E\right)+P\left(E^{\prime }\right)=\frac{1}{2}$

3. $P\left(E\right)=P\left(E^{\prime }\right)$

4. $P\left(E\right)+P\left(E^{\prime }\right)=1$

Q. From a pack of 52 playing cards jack, queen and king of clubs are removed and then well shuffled. From the remaining cards a card is drawn. Find the probability of getting:
i) a face card
ii) a club
iii) a black card
iv) a non face card
v) a king
vi) a red face card
[6 MARKS]

Q.

Gopi buys a fish from a shop for his aquarium. The shopkeeper takes out one fish at random from a tank containing 5 male fish and 8 female fish (see figure). What is the probability that the fish taken out is a male fish?

1. $\frac{5}{13}$

2. $\frac{6}{13}$

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

4. $\frac{8}{15}$

Q.

The chance of getting a doublet with $2$ dice is?

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

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

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

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

Q.

One is asked to select a two -digit number. What is the probability of getting the first digit greater than the second digit ?

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

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

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

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

Q.

In a box containing 18 balls of 3 different colours red, green and blue, if 10 are red and 4 are green, then what is the probability of getting a blue ball in the first attempt?

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

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

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

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

Q.

A student was tested on 100 true or false questions. The number of questions whose answers were true was 59. Find the probability that a question’s answer was false.

1. 0.41

2. 0.59

3. 0.61

4. 1

Q.

A box contains 12 balls out of which $x$ are blue. If one ball is drawn at random from the box, what is the probability that it will be a blue ball ? If 6 more blue balls are put in the box , the probability of drawing a blue ball is now double of what it was before . Find $x$

1. (i) $\frac{x}{12}$ (ii) 3

2. (i) $\frac{x}{6}$ (ii) 4

3. (i) $\frac{x}{6}$ (ii) 5

4. (i) $\frac{x}{4}$ (ii) 2

Q. Question 5
If P(E) = 0.05, what is the probability of ‘not E’?

Q.

You are given a dart board of radius R cm. What is the probability that you hit the bull's eye of radius r cm?

1. $\frac{r}{R}$

2. Insufficient data

3. $\frac{r^2}{R^2}$

4. $\frac{R}{r}$

Q.

A fair die is tossed repeatedly until a six is obtained. Let $X$ denote the number of tosses required. The probability that $X\ge 3$ equals

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

2. $\frac{25}{36}$

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

4. $\frac{25}{216}$

Q. Question 30(i)
All the jacks, queens and kings are removed from a deck of 52 playing cards. The remaining cards are well shuffled and then one card is drawn at random. Giving ace a value 1 similar value for other cards, find the probability that the card has a value 7.

Q.

Three fair coins are tossed simultaneously. Find the probability of getting more heads than the number of tails.

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

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

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

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

Q.

The king, queen and jack are removed from a deck of 52 playing cards and then shuffled. One card is selected from the remaining cards. Find the probability of getting an ace.

Q. Question 18
If a card is selected from a deck of 52 cards, then the probability of its being a red face card is
(a) $\frac{3}{26}$
(b) $\frac{3}{13}$
(c) $\frac{2}{13}$
(d) $\frac{1}{2}$

Q.

An equilateral triangle is drawn with its vertices if we put a dot in it without looking into the picture, find the probability of the dot being outside the triangle?

1. $\frac{4\pi -3\sqrt{3}}{4}$

2. $\frac{4\pi -3\sqrt{3}}{4\pi }$

3. $\frac{\pi -3\sqrt{3}}{4\pi }$

4. $\frac{4\pi -3}{4\pi }$

Q. An equilateral triangle is drawn inside a circle as shown. If we put a dot in it without looking into the picture, find the probability of the dot being outside the triangle?

1. $\frac{4\pi -3\sqrt{3}}{4}$
2. $\frac{4\pi -3\sqrt{3}}{4\pi }$
3. $\frac{\pi -3\sqrt{3}}{4\pi }$
4. $\frac{4\pi -3}{4\pi }$

Q.

Two dice are thrown simultaneously. The probability of getting a doublet is

1. $0$

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

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

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

Q.

5 defective glasses are accidentally mixed with 20 good ones. The good ones and the defective ones look the same from the outside. If a glass is picked at random, what is the probability that the chosen glass is not defective?

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

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

3. $\frac{9}{8}$

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

Q. Question 22
The probability of getting a bad egg in a lot of 400 is 0.035. The number of bad eggs in the lot is
(a) 7
(b) 14
(c) 21
(d) 28

Q. Question 28(i)
The king, queen and jack of clubs are removed from a deck of 52 playing cards and then well shuffled. Now, one card is drawn at random from the remaining cards. Determine the probability that the card is a heart

Q.

Two semicircles are drawn in a square as shown. If we put a dot in the figure, without looking into it, what is the probability of the dot being in the shaded region?

Q.

One card is drawn from a well-shuffled deck of 52 cards. Find the probability of getting

(i) a king of red colour

(ii) a face card

(iii) a red face card

(iv) the jack of hearts

(v) a spade

(vi) the queen of diamonds

Q.

The daily wages of 50 workers in a factory are as follows:

Find the probability that the daily wage of a worker lies in the interval:

i) 110 - 120 ii) 100 - 200 iii) 80 - 120

1. 

2. 

3. 

4. 

5. 

6.