A card is randomly selected from an ordinary deck of playing cards. Find The odd

Question

A card is randomly selected from an ordinary deck of playing cards. Find
The odds in favor of drawing a face card
The odds against drawing a king
The odds in favor of getting a king
The odds against drawing a diamond
The odds against drawing a face card
The odds in favor of drawing a diamond

In an exclusive county club, 68% of the members play bridge and drink champagne. And 83% of members play bridge. If a memeber is selected at random, find the probability the member drinks champagne, given that the member plays bridge. (Keep the anwer with two decimal places)

In a Calculus class there are 11 freshmen and 15 sophomores; 5 of the sophomores are females, and 8 of the freshmen are males. If a student is selected at random.
The probability of selecting a sophomore or a male is
The probability of selecting a sophomore is
The probability of selecting a male is
The probability of selecting a sophomore male is

Explanation / Answer

1. a) P( drawing a face card ) = 12 / 52 = 3/13 since face cards : jack - 4, king - 4, Queen - 4

odds in favor of drawing a face card = 3: 13-3 = 3:10

b) P( drawing a king card ) = 4 / 52 =1 / 13 since kings - 4

odds against of drawing a king card = 13-1 : 1 = 12:1

c)

P( drawing a king card ) = 4 / 52 =1 / 13 since kings - 4

odds favour of drawing a king card = 1:13-1 = 1 :12

d)

P( drawing a diamond card ) = 13 / 52 =1 / 4 since diamonds= 13

odds against of drawing a diamond card = 4-1 : 1 =3:1

e)

P( drawing a face card ) = 12 / 52 = 3/13 since face cards : jack - 4, king - 4, Queen - 4

odds against of drawing a face card = 13-3 : 3 = 10 : 3

f)

P( drawing a diamond card ) = 13 / 52 =1 / 4 since diamonds= 13

odds favour of drawing a diamond card = 1 : 4-1 = 1:3

2)

p(the member drinks champagne/ the member plays bridge)

= P(the member drinks champagne and the member plays bridge) / P(the member plays bridge)

= 0.68 / 0.83 = 0.8193

3)

From the given data,

The probability of selecting a sophomore or a male

= P(sophomore ) + P(male) - P(sophomore and male)

= 15/ 26 + 18/26 - 10/26 = 23/26 =0.8846

The probability of selecting a sophomore is 15/26 = 0.5769

The probability of selecting a male is 18/26 = 0.6923

The probability of selecting a sophomore male is 10/26 = 0.3846

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