Page 100 - DMTH404_STATISTICS

Statistics

Notes From the above table, we can write

 d 500 1
(i) P A Bi  
1000 2

P A  d 250 1
(ii) Bi  
1000 4
 d
P A B  i d 500 + 250 3
(iii) A  Bi  
1000 4
(iv) b  150 +500 250  9
+
P A Bg 
1000 10
This can, alternatively, be written as P A B b g  1 P A  d Bi   100  9 .
1
1000 10
Example 24: What is the probability of drawing a black card or a king from a well-
shuffled pack of playing cards?
Solution.
There are 52 cards in a pack,  n(S) = 52.

Let A be the event that the drawn card is black and B be the event that it is a king. We have to find
 b
P A Bg .
Since there are 26 black cards, 4 kings and two black kings in a pack, we have n(A) = 26, n(B) = 4

+

and (  B = 2n A ) Thus, (A  ) B  26 4 2  7
P
52 13
Alternative Method
The given information can be written in the form of the following table:
B B Total
A 2 24 26
A 2 24 26
Total 4 48 52

From the above, we can write
 b P A  d 24 7
P A Bg   Bi   
1
1
52 13
Example 25: A pair of unbiased dice is thrown. Find the probability that (i) the sum of
spots is either 5 or 10, (ii) either there is a doublet or a sum less than 6.
Solution.
Since the first die can be thrown in 6 ways and the second also in 6 ways, therefore, both can be
thrown in 36 ways (fundamental principle of counting). Since both the dice are given to be
unbiased, 36 elementary outcomes are equally likely.

92 LOVELY PROFESSIONAL UNIVERSITY