Page 110 - DMTH404_STATISTICS

Statistics

Notes (f) Second card is not a spade.

(g) Second card is not a spade given that first is a spade.
(h) The cards are aces or diamonds or both.
Solution.

´
4 48 16
)
(a) P (only first card is a king   .
52 51 221
´
´
æ first card is a jack of ö 5 51 5
(b) P ç ÷   .
è diamond or a king ø 52 51 52
´
æ at least one card isö 40 39 7
´
(c) P ç ÷  1  .
è a picture card ø 52 51 17
´
æ not more than one cardö 40 39 12 40 40 12 210
´
´
´
(d) P  + +  .
ç è is a picture card ÷ ø 52 51 52 51 52 51 221
´
´
´
52 39 13
´
)
(e) P (cards are not of the same suit   .
52 51 17
´
13 39 39 38 3
´
´
)
(f) P (second card is not a spade  +  .
52 51 52 51 4
´
´
æ second card is not a spadeö 39 13
(g) P   .
ç è given that first is spade ø ÷ 51 17
´
æ the cards are aces or ö 16 15 20
(h) P ç ÷   .
´
è diamonds or both ø 52 51 221
Example 37: The odds are 9 : 7 against a person A, who is now 35 years of age, living till
he is 65 and 3 : 2 against a person B, now 45 years of age, living till he is 75. Find the chance that
at least one of these persons will be alive 30 years hence.
Solution.
Note: If a is the number of cases favourable to an event A and a is the number of cases favourable to its
compliment event (a + a = n), then odds in favour of A are a : a and odds against A are a : a.
a a
( ) 
Obviously ( )  and P A .
P A
+
+
a a a a
Let A be the event that person A will be alive 30 years hence and B be the event that person B will
be alive 30 years hence.
7 7 2 2
 P A  and P B 
( )
( ) 
+
+
9 7 16 3 2 5
We have to find P A B b g . Note that A and B are independent.

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