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Questions  >>  CBSE XII  >>  Math  >>  Probability
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Q)

Three events A,B and C have probabilities $\Large \frac{2}{5},\frac{1}{3}$ and $\Large \frac{1}{2}$,respectively.Given that $P(A\cap C)=\frac{1}{5}\;and\;P(B\cap C)=\frac{1}{4}$,find the value of $P(C|B)\; and \;P(A'\cap C').$

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A)
Toolbox:
  • P(C/B)=P\(\frac{(B\cap\;C)}{P(B)}\)
  • P(\(\bar{A}\cap\bar{C}\))=P(\(\overline{A\cup\;C})\)
  • =1-P(A\(\cup\)C)
  • AlsoP(A\(\cup\)C)=P(A)+P(C)-P(A\(\cap\)C)
P(A)=\(\large\frac{2}{3}\)
P(B)=\(\large\frac{1}{3}\)
P(C)=\(\large\frac{1}{2}\)
P(A\(\cap\)C)=\(\large\frac{1}{5}\)
P(B\(\cap\)C)=\(\large\frac{1}{7}\)
P(C/B)=\(\large\frac{1}{7}\times\)\(\large\frac{3}{1}\)=\(\large\frac{3}{7}\)
P(A\(\cup\)C)=\(\large\frac{2}{3}\)+\(\large\frac{1}{2}\)-\(\large\frac{1}{5}\)
=\(\large\frac{29}{30}\)
P(A\(\cap\)C)=1-\(\large\frac{29}{30}\)=\(\large\frac{1}{30}\)

 

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