Question

Let $$A$$ and $$B$$ be two events such that $$P\left( {A \cap B'} \right) = 0.20,\,P\left( {A' \cap B} \right) = 0.15,\,P\left( {A' \cap B'} \right) = 0.1,$$            then $$P\left( {A/B} \right)$$  is equal to :

A. $$\frac{{11}}{{14}}$$  
B. $$\frac{2}{{11}}$$
C. $$\frac{2}{7}$$
D. $$\frac{1}{7}$$
Answer :   $$\frac{{11}}{{14}}$$
Solution :
$$\eqalign{ & P\left( {A \cap B'} \right) = P\left( A \right) - P\left( {A \cap B} \right) = 0.20 \cr & {\text{Also }}P\left( {A' \cap B} \right) = P\left( B \right) - P\left( {A \cap B} \right) = 0.15 \cr & \Rightarrow P\left( A \right) + P\left( B \right) - 2P\left( {A - B} \right) = 0.35 \cr & {\text{Now, }}P\left( {A' \cap B'} \right) = 1 - P\left( {A \cup B} \right) \cr & \Rightarrow 0.1 = 1 - P\left( A \right) - P\left( B \right) + P\left( {A \cap B} \right) \cr & \Rightarrow P\left( A \right) + P\left( B \right) - P\left( {A \cap B} \right) = 0.9 \cr & \Rightarrow P\left( {A \cap B} \right) = 0.9 - 0.35 \cr & \Rightarrow P\left( {A \cap B} \right) = 0.55{\text{ and}} \cr & P\left( A \right) = 0.75,\,P\left( B \right) = 0.70 \cr & {\text{Now, }}P\left( {A/B} \right) = \frac{{P\left( {A \cap B} \right)}}{{P\left( B \right)}} = \frac{{0.55}}{{0.70}} = \frac{{11}}{{14}} \cr} $$

Releted MCQ Question on
Statistics and Probability >> Probability

Releted Question 1

Two fair dice are tossed. Let $$x$$ be the event that the first die shows an even number and $$y$$ be the event that the second die shows an odd number. The two events $$x$$ and $$y$$ are:

A. Mutually exclusive
B. Independent and mutually exclusive
C. Dependent
D. None of these
Releted Question 2

Two events $$A$$ and $$B$$ have probabilities 0.25 and 0.50 respectively. The probability that both $$A$$ and $$B$$ occur simultaneously is 0.14. Then the probability that neither $$A$$ nor $$B$$ occurs is

A. 0.39
B. 0.25
C. 0.11
D. none of these
Releted Question 3

The probability that an event $$A$$ happens in one trial of an experiment is 0.4. Three independent trials of the experiment are performed. The probability that the event $$A$$ happens at least once is

A. 0.936
B. 0.784
C. 0.904
D. none of these
Releted Question 4

If $$A$$ and $$B$$ are two events such that $$P(A) > 0,$$   and $$P\left( B \right) \ne 1,$$   then $$P\left( {\frac{{\overline A }}{{\overline B }}} \right)$$  is equal to
(Here $$\overline A$$ and $$\overline B$$ are complements of $$A$$ and $$B$$ respectively).

A. $$1 - P\left( {\frac{A}{B}} \right)$$
B. $$1 - P\left( {\frac{{\overline A }}{B}} \right)$$
C. $$\frac{{1 - P\left( {A \cup B} \right)}}{{P\left( {\overline B } \right)}}$$
D. $$\frac{{P\left( {\overline A } \right)}}{{P\left( {\overline B } \right)}}$$

Practice More Releted MCQ Question on
Probability


Practice More MCQ Question on Maths Section