Probability of solving specific problem independently by A and B … - Vidyadip

Question

Probability of solving specific problem independently by A and B are $\frac{1}{2}$ and $\frac{1}{3}$ respectively. If both try to solve the problem independently, find the probability that, exactly one of them solve the problem.

✓

Answer

$A$ and $B$ are independently try to solve problem with probability
$\begin{array}{l}
P(A)=\frac{1}{2} \\
P(B)=\frac{1}{3}
\end{array}$
Which are independent events.
$\therefore P(A \cap B)=P(A) \cdot P(B)$
$\rightarrow$ Exactly one of them solves the problem
$\begin{array}{l}
=P\left(A \cap B^{\prime}\right)+P\left(A^{\prime} \cap B\right) \\
=P(A)-P(A \cap B)+P(B)-P(A \cap B) \\
=P(A)+P(B)-2 P(A) P(B) \\
=\frac{1}{2}+\frac{1}{3}-2 \times \frac{1}{2} \times \frac{1}{3} \\
=\frac{1}{2}+\frac{1}{3}-\frac{1}{3} \\
=\frac{1}{2}
\end{array}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "2 Marks" from JUNE 2024→JUNE 2024 — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Evaluate:
$\sin\Big(\tan^{-1}\text{x}+\tan^{-1}\frac{1}{\text{x}}\Big)\text{ for }\text{x}<0$

Find the domain of the following functions:
$\text{f(x)}=\sin^{-1}\text{x}+\sin\text{x}$

Find the area bounded by the curve $y=x^3-6 x^2+$ $8 x, x=a, x=b$ and the $x$-axis.

Find the magnitude of two vectors $\vec{a}\ \text{and}\ \vec{b},$ having the same magnitude and such that the angle between them is 60° and their scalar product is $\frac{1}{2}\cdot$

Find $\big|\vec{\text{a}}-\vec{\text{b}}\big|$ if
$|\vec{\text{a}}|=2,\big|\vec{\text{b}}\big|=5$ and $\vec{\text{a}}.\vec{\text{b}}=8$

Evaluate the following:
$\tan\Big(\cos^{-1}\frac{8}{17}\Big)$

Evaluate the following integrals:
$\int3^{2\log_3\text{x}}\text{dx}$

If $\text{f(x)}=\log_\text{e}(\log_\text{e}\text{x}),$ then write the value of f'(e).

If $\vec{\text{a}}$ and $\vec{\text{b}}$ are two vectors of magnitudes 3 and $\frac{\sqrt{2}}{3}$ repectively such that $\vec{\text{a}}\times\vec{\text{b}}$ is a unit vector. write the angle between $\vec{\text{a}}$ and $\vec{\text{b}}.$

Is every continuous function differentiable?