Page 80 - DMTH404_STATISTICS

Statistics

Notes
Example 6: Find the probability of throwing a total of six in a single throw with two
unbiased dice.
Solution.
The number of exhaustive cases n = 36, because with two dice all the possible outcomes are :
(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6),

(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6),
(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6),
(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6),
(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6),

(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6).
Out of these outcomes the number of cases favourable to the event A of getting 6 are : (1, 5),
(2, 4), (3, 3), (4, 2), (5, 1). Thus, we have m = 5.

5
( ) =
 P A .
36

Example 7: A bag contains 15 tickets marked with numbers 1 to 15. One ticket is drawn
at random. Find the probability that
(i) the number on it is greater than 10,

(ii) the number on it is even,
(iii) the number on it is a multiple of 2 or 5.
Solution.
Number of exhaustive cases n = 15

(i) Tickets with number greater than 10 are 11, 12, 13, 14 and 15. Therefore, m = 5 and hence the
5 1
required probability = = .
15 3
(ii) Number of even numbered tickets m = 7

7
 Required probability = .
15
(iii) The multiple of 2 are : 2, 4, 6, 8, 10, 12, 14 and the multiple of 5 are : 5, 10, 15.
 m = 9 (note that 10 is repeated in both multiples will be counted only once).

9 3
Thus, the required probability = = .
15 5

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