in a single cast with two dice the odds against drawing 7

In a single cast with two dice the odds against drawing $$7$$ is :

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

B. $$\frac{1}{{12}}$$

C. $$5:1$$

D. $$1:5$$

Answer : $$5:1$$

Solution :
$$E = \left\{ {\left( {1,\,6} \right),\,\left( {2,\,5} \right),\,\left( {3,\,4} \right),\,\left( {4,\,3} \right),\,\,\left( {5,\,2} \right)\left( {6,\,1} \right)} \right\}$$
$$\therefore \,P\left( E \right) = \frac{6}{{6 \times 6}} = \frac{1}{6}.$$ So, the odds against drawing $$7 = \frac{{P\left( {\overline E } \right)}}{{P\left( E \right)}} = \frac{{1 - \frac{1}{6}}}{{\frac{1}{6}}} = \frac{5}{1}.$$

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

In a single cast with two dice the odds against drawing $$7$$ 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).

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In a single cast with two dice the odds against drawing $$7$$ 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).

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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