Answered

Seventy cards are numbered 1 through 70 , one number per card. One card is randomly selected from the deck. What is the probability that the number drawn is a multiple of 3 AND a multiple of 5 ?

Answer :

MrRoyal

Answer:

[tex]Probability = \frac{2}{35}[/tex]

Step-by-step explanation:

Given

[tex]Total = 70[/tex]

First, we need to list the multiples of 5

[tex]M_5 = \{5,10,15,20,25,30,35,40,45,50,55,60,65,70\}[/tex]

Then, multiples of 3[tex]M_3 = \{3,6,9,12,15,18,21,24,27,30,33,36,39,42,45,48,51,54,57,60,63,66,69\}[/tex]

Next, is to list out the common elements in both

[tex]M_3\ n\ M_5 = \{15,30,45,60\}[/tex]

[tex]n(M_3\ n\ M_5) = 4[/tex]

The required probability is then calculated as thus:

[tex]Probability = \frac{n(M_3\ n\ M_5)}{Total}[/tex]

[tex]Probability = \frac{4}{70}[/tex]

[tex]Probability = \frac{2}{35}[/tex]

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