Question

If A and B are the events such that p(A)=1/4, p(B)=1/2, p(AnB)=1/6 find p(A or B) (b)p(A but not B) (c)p(not A and not B)
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Answer 1

Answer:

a)P(A or B) = P(A u B)

= P(A) + P(B) - P(A n B)

$= \frac{1}{4} + \frac{1}{2} - \frac{1}{6}$

$= \frac{3 + 6 - 2}{12}$

$\frac{7}{12}$

b) P(A but not B)

= P(A) - P(A n B)

$= \frac{1}{4} - \frac{1}{6}$

$= \frac{6 - 4}{24}$

$= \frac{2}{24}$

$= \frac{1}{12}$

c) P(not A and not B) =

$= 1 - ( \frac{1}{4} + \frac{1}{2} )$

$= \frac{3}{4}$

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