7 conditional prob Five cards are dealt off the top of a wel

7. (conditional prob.) Five cards are dealt off the top of a well-shuffed deck. (a) Find the chance that the 5th card is the queen of spade (b) Find the chance that the 5th card is the queen of spades, given that the first 4 cards are hearts. 8. A coin is tossed 3 times. (a) What is the chance of getting 3 heads? (b) What is the chance of not getting 3 heads? (c) What is the chance of getting at least 1 tail? (d) What is the chance of getting at least 1 head? 9. Every week you buy a ticket in a lottery that offers once chance in a million of winning. What is the chance that you never win, even if you keep htis up for 10 years.

Solution

note : only one question is allowed per submission

7 . a .

number of queen of spades = 1 out of 52 cards .

now the chance of the 5th card to be queen of spade = 1/52

since , nothing is told about first 4 cards,, so assume they are sure events with probability of 1

, hence = 1/52

b. 5th is queen of spades where first 4 are hearts

number of hearts in deck of card = 13

now the prob of 1st heart = 13/52

now the prob of 2nd heart = 12/52

now the prob of 3rd heart = 11/52

now the prob of 4th heart = 10/52

5t card is queen of spades = 1/52

therefore total prob is

(13/52 )*(12/52 )*(11/52 )*(10/52 )* 1