Page 109 - DMTH404_STATISTICS

Unit 7: Modern Approach to Probability

10
(a) Two red balls can be drawn from 10 red balls in C ways. Notes
2
10!
 n A 10 C   45
( ) 
2
2!8!
( )
n A 45 5
Thus, P A  
( ) 
n ( ) S 153 17
10
8
(b) One red ball can be drawn in C ways and one black ball can be drawn in C ways.
1 1
80
10
8
 n ( ) B  C ´ C  10 8  80 Thus, P B a f = 153
´
1
1
Example 35:
Five cards are drawn in succession and without replacement from an ordinary deck of 52 well-
shuffled cards:
(a) What is the probability that there will be no ace among the five cards?
(b) What is the probability that first three cards are aces and the last two cards are kings?
(c) What is the probability that only first three cards are aces?
(d) What is the probability that an ace will appear only on the fifth draw?
Solution.

48 47 ´ 46 45 44
´
´
´
)
(a) P (there is no ace   0.66
´
´
´
´
52 51 50 49 48
´
´
´
´
æ first three card are aces and ö 4 3 2 4 3
(b) P ç ÷   0.0000009
´
´
´
´
è the last two are kings ø 52 51 50 49 48
4 3 2 48 47
´
´
´
´
)
(c) P (only first three card are aces   0.00017
´
´
´
´
52 51 50 49 48
´
´
æ an ace appears only ö 48 47 ´ 46 45 4
´
(d) P   0.059
ç è on the fifth draw ø ÷ 52 51 50 49 48
´
´
´
´
Example 36:
Two cards are drawn in succession from a pack of 52 well-shuffled cards. Find the probability
that:
(a) Only first card is a king.
(b) First card is jack of diamond or a king.
(c) At least one card is a picture card.
(d) Not more than one card is a picture card.
(e) Cards are not of the same suit.
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