Page 347 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_ENGLISH

Statistical Methods in Economics

Notes 6 1
= +
15 15
7
=
15
Example 3: Find the probability of getting more than 4 in tossing a die.
Solution: The numbers more than 4 on a die are 5 and 6.
Let A and B be the respective events of getting 5 and 6.

1 1
Thus, P (A) = , P (B) =
6 6
Also A and B are mutually exclusive.
1 1 2 1
Thus, P (A or B) = P (A) + P (B) = + = =
6 6 6 3
Example 4: A card is drawn at random from a well-shuffled pack of 52 cards. Find the probability
of getting an ace or a spade.
Solution: Let A be the event of getting an ace and B of getting a spade. Then A = set of all aces,
B = set of all spades and A ∩ B = set of an ace of spade.

)A ∩
Clearly, n (A) = 4, n (B) = 13 and n( B = 1.
Also, n (S) = 52. Therefore,

n ( ) 4 n () 13 n (A I B ) 1
B
A
P (A) = = , P (B) = = and P ( I B = =
)A
n () S 52 n () S 52 n () S 52
Thus, the required probability
P (an ace or a spade) = P (A or B) = ( PA ∪ B = P (A) + P (B) − ( ∩PA B )
)
4 13 1 16 4
= + − = =
52 52 52 52 13
Example 5: A construction company is bidding for two contracts, A and B. The probability that
the company will get contract A is 3/5, will get contract B is 1/4 and the probability
that the company gets both the contracts is 1/8. What is the probability that the
company will get contract A or B ?
Solution: Let A and B be the respective events of getting the contracts A and B. Then, we are
given that
P (A) = 3/5, (B) = 1/4 and ( PA ∩ B = 1/8
)
Thus, the required probability that the company will get a contract A or B is
P (A or B) = ( PA ∪ B = P (A) + P (B) − ( ∩ PA ) B
)
3 1 1 29
= + − =
5 4 8 40
Example 6: A bag contains 30 balls numbered from 1 to 30. One ball is drawn at random. Find the
probability that number of the drawn ball is a multiple of (i) 4 or 9 (ii) 5 or 6.
Solution: (i) Let A be the event that the drawn number is a multiple of 4, then A = {4, 8, 12, 16,
20, 24, 28}. Further let B be the event that the drawn number is a multiple of 9, i.e.,
B = {9, 18, 27}.

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