Question

An urn contains nine balls of which three are red, four are blue and two are green. Three balls are drawn at random without replacement from the urn. The probability that the three balls have different colours is

A. $$\frac{2}{{7}}$$  
B. $$\frac{1}{{21}}$$
C. $$\frac{2}{{23}}$$
D. $$\frac{1}{{3}}$$
Answer :   $$\frac{2}{{7}}$$
Solution :
$$n\left( S \right) = {\,^9}{C_3},n\left( E \right) = {\,^3}{C_1} \times {\,^4}{C_1} \times {\,^2}{C_1}$$
Probability $$ = \frac{{3 \times 4 \times 2}}{{^9{C_3}}}$$
$$\eqalign{ & = \frac{{24 \times 3!}}{{9!}} \times 6! \cr & = \frac{{24 \times 6}}{{9 \times 8 \times 7}} \cr & = \frac{2}{7} \cr} $$

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. $$\frac{{P\left( {\overline A } \right)}}{{P\left( {\overline B } \right)}}$$

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