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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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Give your answer to three decimal places.
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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

Respuesta :

MrRoyal

Answer:

(1) [tex]P(Heart\ and\ Club) = 0.0494[/tex]

(2) [tex]S = \{B,B,B,B,R,R,R,R,R,Y,Y,Y,Y,Y,Y,Y,Y\}[/tex]

Step-by-step explanation:

Question 1:

Given

[tex]Hearts = 8[/tex]

[tex]Diamond = 3[/tex]

[tex]Club=2[/tex]

[tex]Spade = 5[/tex]

[tex]Total = 18[/tex]

Required

Probability of 1 heart and 1 club

This probability is calculated as:

[tex]P(Heart\ and\ Club) = P(Heart) * P(Club)[/tex]

[tex]P(Heart\ and\ Club) = \frac{n(Heart)}{Total} * \frac{n(Club)}{Total}[/tex]

[tex]P(Heart\ and\ Club) = \frac{8}{18} * \frac{2}{18}[/tex]

[tex]P(Heart\ and\ Club) = \frac{8*2}{18*18}[/tex]

[tex]P(Heart\ and\ Club) = \frac{16}{324}[/tex]

[tex]P(Heart\ and\ Club) = 0.0494[/tex] -- approximated

Question 2:

Given

[tex]Blue = 4[/tex]

[tex]Red= 5[/tex]

[tex]Yellow = 8[/tex]

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:

[tex]S = \{B,B,B,B,R,R,R,R,R,Y,Y,Y,Y,Y,Y,Y,Y\}[/tex]

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