Download App

Probability — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSProbability1 Mark
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 the problem is solved.
✓

Answer

Given:
P(A) = Probability of solving the problem by A = $\frac{1}{2}$
P(B) = Probability of solving the problem by B = $\frac{1}{3}$
Since, A and B both are independent.
$\Rightarrow$ P(A $\cap$ B) = P(A).P(B)
$\Rightarrow$ P (A $\cap$ B) = $\frac{1}{2} \times \frac{1}{3}=\frac{1}{6}$ 
The problem is solved, i.e. it is either solved by A or it is solved by B.
= P(A $\cup$ B)
As we know, P (A $\cup$ B) = P(A) + P(B) - P (A $\cap$ B)
⇒ P (A $\cup$ B) = $\frac{1}{2}+\frac{1}{3}-\frac{1}{6}=\frac{4}{6}$ 
$\Rightarrow \mathrm{P}(\mathrm{A} \cup \mathrm{B})=\frac{2}{3}$

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 "1 Marks Question" from Probability→Probability — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

Write the degree of the differrntial equation $\frac{\text{d}^{2}\text{y}}{\text{dx}^{2}}+3\Big(\frac{\text{dy}}{\text{dx}}\Big)^{2}=\text{x}^{2}\log\Big(\frac{\text{d}^{2}\text{y}}{\text{dx}^{2}}\Big).$ 
→
Integrate the function $\frac{x^{2}+x+1}{(x+1)^{2}(x+2)}$
→
Area bounded by the curve $y = x^3,$ the $x-$axis and the ordinates $x = -2$ and $x = 1$ is
→
Find the value of the expression $\tan \left( {{{\sin }^{ - 1}}\frac{3}{5} + {{\cot }^{ - 1}}\frac{3}{2}} \right)$.
→
Find the interval of the function that is strictly increasing or decreasing: $(x + 1)^3 (x - 3)^{3 }$
→
An edge of a variable cube is increasing at the rate of $5 cm$ per second. How fast is the volume increasing when the side is $15 cm$.
→
If $\text{f}(\text{x}) = \int\limits_{0}^{\text{x}}\text{t}\sin\text{t }\text{dt},$then write the value of f'(x).
→
The interval in which $y = x^2 e^{–x}$ is increasing is
→
Construct a 4 × 3 matrix whose element are:
$\text{a}_\text{ij}=\frac{\text{i}-\text{j}}{\text{i}+\text{j}}$
→
A fair die is rolled. Consider events E = {1,3,5}, F = {2,3} and G = {2,3,4,5}.
Find P(E|G) and P(G|E)
→