Download App

Probability — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsProbability5 Marks
Question
Given the probability that A can solve a problem is $\frac{2}{3}$ and the probability that B can solve the same problem is $\frac{3}{5}$. Find the probability that none of the two will be able to solve the problem.
✓

Answer

Given,
Probability that A can solve a problem $=\frac{2}{3}$
$\Rightarrow\ \text{P(A)}=\frac{2}{3}$
$=\text{P}(\overline{\text{A}})=1-\frac{2}{3}$
$\text{P}(\overline{\text{A}})=\frac{1}{3}$
Probability that B can solve the same problem $=\frac{3}{5}$
$\Rightarrow\ \text{P(B)}=\frac{3}{5}$
$\Rightarrow\ \text{P}(\overline{\text{B}})=1-\frac{3}{5}$
$\text{P}(\overline{\text{B}})=\frac{2}{5}$
P(None of them solve the problem)
$=\text{P}(\overline{\text{A}}\cap\overline{\text{B}})$
$=\text{P}(\overline{\text{A}})\text{ P}(\overline{\text{B}})$
$=\frac{1}{2}\times\frac{2}{5}$
$=\frac{2}{15}$
Required probability $=\frac{2}{15}$

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 "5 Marks Questions" from Probability→Probability — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

A chemical company produces two compounds, $A$ and $B.$ The following table gives the units of ingredients, $C$ and $D$ per kg of compounds $A$ and $B$ as well as minimum requirements of $C$ and $D$ and costs per kg of $A$ and $B$. Find the quantities of $A$ and $B$ which would give a supply of $C$ and $D$ at a minimum cost.
 
Compound
Minimum requirement
$A$
$B$
 
Ingredient $C$
$1$
$2$
$80$
Ingredient $D$
$3$
$1$
$75$
Coist $($in Rs.$)$ per Kg
$4$
$6$
  
→
Evaluate the following integrals:$\int\text{x}\tan^2\text{x dx}$
→
Evaluate the following intregals:
$\int\frac{5\text{x}}{(\text{x}+1)(\text{x}^2-4)}\text{dx}$
→
Differentiate the following functions from first principles:
$\text{e}^{\sqrt{2\text{x}}}$
→
A man 160cm tall, walks away from a source of light situated at the top of a pole 6m high, at the rate of 1.1m/ sec. How fast is the length of his shadow increasing when he is 1m away from the pole?
→
Solve the following differential equation:
$\frac{\text{dy}}{\text{dx}}=\frac{\text{y}}{\text{x}}-\sqrt{\frac{\text{y}^2}{\text{x}^2}-1}$
→
using interation, find the area of the region bounded by the triangle ragion, the euations of whose sides are $y = 2x + 1, y = 3x + 1$ and $x = 4$.
→
A letter is known to have come either from LONDON or CLIFTON. On the envelope just two consecutive letters ON are visible. What is the probability that the letter has come from,
LONDON.
→
Evaluate the following integrals:
$\int\limits^\frac{\pi}{2}_{0}\frac{\cos^2\text{x}}{1+3\sin^3\text{x}}\text{ dx}$
→
Using differentials, find the approximate values of the following:
$\Big(\frac{17}{81}\Big)^{\frac{1}{4}}$
→