Paper 4: Fundamentals of Business Mathematics & Statistic

9.4 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS

Probability

Example 1:

What is the chance of getting a king in a draw from a pack of 52 cards?

Solution:

The total number of cases that can happen

= 52 (52 cards are there).

Total number of kings are 4 ; hence favourable cases=4 Therefore probability of drawing a king =52 134 1=.

Example 2:

Two coins are tossed simultaneously. What is the probability of getting a head and a tail?

Solution :

The possible combinations of the two coins turning up with head (H) or tail (T) are HH, HT, TH, TT. The favourable

ways are two out of these four possible ways and all these are equally likely to happen.

Hence the probability of getting a head and a tail is 2 14 2=.

Example 3 :

One card is drawn at random from a well-shuffled pack of 52 cards. What is the probability that it will be (a)

a diamond (b) a queen?

Solution:

(a) There are 13 diamond cards in a pack of 52 cards. The number of ways in which a card can be drawn

from that pack is 52. The number favourable to the event happening is 13.

Hence probability of drawing a diamond

13 1

52 4=

(b) There are 4 queens in the pack ; and so the number of ways favourable to the event = 4

The probability = 52 134 1=

Example 4 :

Two cards are drawn from a pack of cards at random. What is the probability that it will be (a) a diamond

and a heart (b) a king and a queen (c) two kings?

Solution:

(a) The number of ways of drawing 2 cards from out of 52 cards

(^52) C 2 52 51 26 51
1 2

= = × = ×

×

The number of ways of drawing a diamond and a heart

=13 x 13

The required probability

13 13 13

26 51 102

= × =

×