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From the sample space S=(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15) a single number is to be selected at random. Given event A, that the selected number is even, and event B, that the selected number is a multiple of 4, find P(AIB)​

Sagot :

MrRoyal

Answer:

[tex]P(A|B) = 1[/tex]

Step-by-step explanation:

Given

[tex]S = \{1,2,3,4,5,6,7,8,9,10,11,12,13,14,15\}[/tex]

[tex]A = \{2,4,6,8,10,12,14\}[/tex]

[tex]P(A) = 7/15[/tex]

[tex]B = \{4,8,12\}[/tex]

[tex]P(B) = 3/15[/tex]

Required

[tex]P(A|B)[/tex]

This is calculated as:

[tex]P(A|B) = \frac{P(A\ n\ B)}{P(B)}[/tex]

Where

[tex]A\ n\ B = \{4,8,12\}[/tex]

[tex]P(A\ n\ B) = 3/15[/tex]

So, we have:

[tex]P(A|B) = \frac{P(A\ n\ B)}{P(B)}[/tex]

[tex]P(A|B) = \frac{3/15}{3/15}[/tex]

[tex]P(A|B) = 1[/tex]

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