five horses are in a race mr a selects two of the horses at

Five horses are in a race. Mr. $$A$$ selects two of the horses at random and bets on them. The probability that Mr. $$A$$ selected the winning horse is

A. $$\frac{2}{5}$$

B. $$\frac{4}{5}$$

C. $$\frac{3}{5}$$

D. $$\frac{1}{5}$$

Answer : $$\frac{2}{5}$$

Solution :
Let 5 horses are $${H_1},$$ $${H_2},$$ $${H_3},$$ $${H_4},$$ and $${H_5}.$$ Selected pair of horses will be one of the 10 pairs $$\left( {{\text{i}}{\text{.e}}{\text{.;}}{{\text{ }}^5}{C_2}} \right):{H_1}{H_2},$$ $${H_1}{H_3},$$ $${H_1}{H_4},$$ $${H_1}{H_5},$$ $${H_2}{H_3},$$ $${H_2}{H_4},$$ $${H_2}{H_5},$$ $${H_3}{H_4},$$ $${H_3}{H_5},$$ and $${H_4}{H_5}.$$
Any horse can win the race in 4 ways.
For example : Horses $${H_2}$$ win the race in 4 ways $${H_1}{H_2},$$ $${H_2}{H_3},$$ $${H_2}{H_4},$$ and $${H_2}{H_5}.$$
Hence required probability $$ = \frac{4}{{10}} = \frac{2}{5}$$

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

Five horses are in a race. Mr. $$A$$ selects two of the horses at random and bets on them. The probability that Mr. $$A$$ selected the winning horse 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

Five horses are in a race. Mr. $$A$$ selects two of the horses at random and bets on them. The probability that Mr. $$A$$ selected the winning horse 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