Probabilities of a problem being solved by two students are frac{1}{2},frac{1}{3} . Then probability

English

Gujarati

Hindi

14.Probability

medium

The probabilities of a problem being solved by two students are $\frac{1}{2},\frac{1}{3}$. Then the probability of the problem being solved is

A

$\frac{2}{3}$

B

$\frac{4}{3}$

C

$\frac{1}{3}$

D

$1$

Solution

(a) The probability that the problem is not being solved by any of two students

$= \left( {1 – \frac{1}{2}} \right)\,\left( {1 – \frac{1}{3}} \right) = \frac{1}{3}$ and

probability that the problem is solved $= 1 – \frac{1}{3} = \frac{2}{3}$.

Standard 11

Mathematics

Share

Similar Questions

Two dice are thrown. The events $A, B$ and $C$ are as follows:

$A:$ getting an even number on the first die.

$B:$ getting an odd number on the first die.

$C:$ getting the sum of the numbers on the dice $\leq 5$

Describe the events $A$ or $B$

medium

A coin is tossed twice. The probability of getting head both the times is

easy

Consider the experiment of rolling a die. Let $A$ be the event 'getting a prime number ', $B$ be the event 'getting an odd number '. Write the sets representing the events $^{\prime}$ not $A\,^{\prime}$.

easy

Two dice are thrown. The events $A,\, B$ and $C$ are as follows:

$A:$ getting an even number on the first die.

$B:$ getting an odd number on the first die.

$C:$ getting the sum of the numbers on the dice $\leq 5$

State true or false $:$ (give reason for your answer)

Statement : $A$ and $B$ are mutually exclusive

medium

Two dice are thrown. The events $A, B$ and $C$ are as follows:

$A:$ getting an even number on the first die.

$B:$ getting an odd number on the first die.

$C:$ getting the sum of the numbers on the dice $\leq 5$

Describe the events $A$ and $B$

medium