Page 269 - ICSE Math 8

Deck of playing cards

A deck of playing cards has in all 52 cards. It has 13 cards of each of 4 suits, namely spades, clubs, hearts
and diamonds.
(i) Cards of spades and clubs are black cards.
(ii) Cards of hearts and diamonds are red cards.
♠ ♣ ♥ ♦

Spades Clubs Hearts Diamonds

(iii) Kings, queens and jacks (or knaves) are known as face cards. Thus, there are in all 12 face cards.

King queen Jack

Theoretical Probability

If there are n outcomes of a random experiment and out of these, m outcomes are favourable to an event A,
then the probability of happening of event A is denoted by P(A) and is defined as:

Number of favourable outcomes A m
P(A) = =
Total numberof possible outcomees n

• 0 ≤ P(A) ≤ 1, i.e., probability of happening or not happening of an event lies between 0 and 1.
• P(A) + P(A) = 1, i.e., P(A) = 1 – P(A) or P(A) = 1 – P(A)

Example 1: A fair die is rolled once. What is the probability of getting a Try These
number less than 7?

Solution: When a fair die is rolled once, the possible outcomes are 1, 1. A fair coin is tossed. What
2, 3, 4, 5 and 6. is the probability of getting
a head?
\ Total outcomes = 6. 2. If a coin is tossed twice, what

Numbers less than 7 are 1, 2, 3, 4, 5, 6. is the probability of getting a
So, favourable outcomes = 6 Head (H) and a Tail (T)?
Favourable outcom 6
Hence, probability of getting a number less than 7= = = 1
Total outcomes 6
Thus, the probability of getting a number less then 7 is 1, which means it is a sure event, i.e.,
any outcome will be less than 7.

Example 2: A coin is tossed 50 times and head appears 30 times. What is the probability of getting a tail?
Solution: Total number of trials = 50
Number of times head appeared = 30
\ Number of times tail appeared = 50 – 30 = 20

Number of times tail appeared 20 2
Probability of getting a tail = = =
Total numberoftrials 50 5

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