PROBABILITY
IMPORTANT FACTS AND FORMULAE
1. Experiment:
An operation which can produce some well-defined outcomes is called an experiment.
2. Random Experiment: An experiment in which all possible outcomes are known and exact output
cannot be predicted in advance, is called a random experiment.
2. Examples of Performing a Random Experiment:
(i). Rolling an unbiased dice.
(ii). Tossing a fair coin.
(iii). Drawing a card from a pack of well-shuffled cards.
(iv). Picking up a ball of certain colour from a bag containing balls of different colours
Details :
(i). When we throw a coin. Then either a Head (H) or a Tail (T) appears.
(ii). A dice is a solid cube, having 6 faces, marked 1, 2, 3, 4, 5, 6 respectively.
When we throw a die, the outcome is the number that appears on its upper face.
3. Sample space: When we perform an experiment, then the set S of all possible outcomes is called
the Sample Space. Examples of Sample Spaces:
(i). In tossing a coin, S = {H, T}.
(ii). If two coins are tossed, then S = {HH, HT, TH, TT}.
(iii). In rolling a dice, we have, S = {1, 2, 3, 4, 5, 6}.
4. Event :
Any subset of a sample space is called an event.
5. Probability of Occurrence of an Event: Let S be the sample space and let E be an event.
Therefore, P(E)= n(E)/n(S).
PROBLEMS
1). In a throw of a coin, find the probability of getting head?
a) 3/2 b) 3/4
c) 1/2 d) 1
2). Two unbiased coins are tossed. What is the probability of getting exactly 1 tail?
a) 3/4 b) 1/2
c) 2/4 d) 1
3). Two unbiased coins are tossed. What is the probability of getting 2 tail?
a) 3/4 b) 1/2
c) 1/4 d) 1
4). Two unbiased coins are tossed. What is the probability of getting at least one head?
a) 3/4 b) 1/4
c) 1/2 d) 1
5). Three unbiased coins are tossed. What is the probability of getting at least 2 heads?
a) 1/4 b) 1/2
c) 1/3 d) ⅛
6). Three unbiased coins are tossed. What is the probability of getting at least all are heads?
a) 1/4 b) 1/2
c) 1/8 d) ⅛
7). Three unbiased coins are tossed. What is the probability of getting at No heads?
a) 1/4 b) 1/2
c) 1/3 d) ⅛
8). Three unbiased coins are tossed. What is the probability of getting atleast 1 head and tail ?
a) 1/4 b) 1/2
c) 1/3 d) ⅛
9). 4 unbiased coins are tossed. What is the probability of getting all are heads?
a) 1/4 b) 1/2
c) 1/3 d) ⅛
10). An unbiased die is tossed. Find the probability of getting multiple of 3?
a) 1/6 b) 2/3
c) 1/2 d) ⅓
11). In a simultaneous throw of a pair of dice, find the probability of getting a total more than 7?
a) 5/12 b) 3/12
c) 7/12 d) 9/12
12). In a simultaneous throw of a pair of dice, find the probability of getting a total 12 ?
a) 5/12 b) 3/12
c) 7/12 d) 1/36
13). What is the probability of getting a sum 9 from two throws of a dice?
a) 1/6 b) 1/8
c) 1/9 d) 1/12
14). In a simultaneous throw of two dice, what is the probability of getting a doublet?
a) 1/6 b) ¼ c) 2/3 d) 3/7
15). A bag contains 6 black & 8 white balls. One ball is drawn at random. What is the probability that
the ball drawn is white?
a) 3/4 b) 4/7
c) 1/8 d) 3/7
16). In a simultaneous throw of two die, what is the probability of getting a total of 10 or 11?
b) 1/4 b) 1/6
c) 7/12 d) 5/36
17). A bag contains 4 white, 5 red and 6 blue balls. Three balls are drawn at random from the
bag. The probability that all of them are red, is:
a).2/91 b.)11/21 c)2/7 d)5/7
18).A bag contains 2 red, 3 green and 2 blue balls. Two balls are drawn at random. What is the
probability that none of the balls drawn is blue?
a).10/21 b.)11/21 c)2/7 d)5/7
19). In a class, there are 15 boys and 10 girls. Three students are selected at random. The
probability that 1 girl and 2 boys are selected, is:
a).21/46 b.)11/21 c)2/7 d)5/7
20). In a lottery, there are 10 prizes and 25 blanks. A lottery is drawn at random. What is the
probability of getting a prize?
a).2/7 b.)11/21 c)2/7 d)5/7
21).From a shuffled pack of cards, John picks up one card at random. What
is the probability of it being a hearts' card?
a).2/7 b.)11/21 c)2/7 d)1/4
22) One card is drawn at random from a pack of 52 cards. What is the probability that the card drawn is a
face card?
c) 1/13 b) 4/13
c) 1/14 d) 9/52
23).Two cards are drawn together from a pack of 52 cards. The probability that one is a spade
and one is a heart, is:
a). 13/102 b.)11/21 c)2/7 d)5/7
