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A shuffled deck of cards is placed face-down on the table. It contains 8 hearts, 3 diamonds, 2 clubs and 5 spades. What
is the probability that the top two cards are one of the hearts followed by one of the clubs?
Question 2
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A bag has 4 blue balls, 5 red and 8 yellow. A ball is picked at random from the bag.
State the sample space.
Question 3

Answer 1

(1)
`P(Heart\ and\ Club) = 0.0494`

(2)
`S = \{B,B,B,B,R,R,R,R,R,Y,Y,Y,Y,Y,Y,Y,Y\}`

Explanation:

Question 1:

Given

`Hearts = 8`

`Diamond = 3`

`Club=2`

`Spade = 5`

`Total = 18`

Required

Probability of 1 heart and 1 club

This probability is calculated as:

`P(Heart\ and\ Club) = P(Heart) * P(Club)`

`P(Heart\ and\ Club) = (n(Heart))/(Total) * (n(Club))/(Total)`

`P(Heart\ and\ Club) = (8)/(18) * (2)/(18)`

`P(Heart\ and\ Club) = (8*2)/(18*18)`

`P(Heart\ and\ Club) = (16)/(324)`

`P(Heart\ and\ Club) = 0.0494` -- approximated

Question 2:

Given

`Blue = 4`

`Red= 5`

`Yellow = 8`

Required

Determine the sample space

Represent the blue balls with B, the red with R and the yellow with Y.

The sample space (S) is:

`S = \{B,B,B,B,R,R,R,R,R,Y,Y,Y,Y,Y,Y,Y,Y\}`