three identical dice are rolled the probability that the

Three identical dice are rolled. The probability that the same number will appear on each of them is

A. $$\frac{1}{6}$$

B. $$\frac{1}{36}$$

C. $$\frac{1}{18}$$

D. $$\frac{3}{28}$$

Answer : $$\frac{1}{36}$$

Solution :
Favourable cases $$ = 6;\left\{ {\left( {1,1,1} \right),\left( {2,2,2} \right),.....\left( {6,6,6} \right)} \right\}$$
Total cases $$ = 6 \times 6 \times 6 = 216$$
$$\therefore \,\,{\text{Req}}{\text{. prob}}{\text{. = }}\frac{6}{{216}} = \frac{1}{{36}}$$

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

View Answer

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

View Answer

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

View Answer

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

View Answer

Three identical dice are rolled. The probability that the same number will appear on each of them is

Releted MCQ Question on
Statistics and Probability >> Probability

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:

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

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

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).

Practice More Releted MCQ Question on
Probability

Practice More MCQ Question on Maths Section

Three identical dice are rolled. The probability that the same number will appear on each of them is

Releted MCQ Question on Statistics and Probability >> Probability

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:

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

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

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).

Practice More Releted MCQ Question on Probability

Practice More MCQ Question on Maths Section

Releted MCQ Question on
Statistics and Probability >> Probability

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).

Practice More Releted MCQ Question on
Probability