The probability that a student selected at random from a class wi… - Vidyadip

Question

The probability that a student selected at random from a class will pass in Mathematics is $\frac{4}{5}$, and the probability that he/ she passes in Mathematics and Computer Science is $\frac{1}{2}$. What is the probability that he/ she will pass in Computer Science if it is known that he/ she has passed in Mathematics?

✓

Answer

Given,
Probability to pass mathen atics (M)
$\text{P(M)}=\frac{4}{5}$
Probability to pass in mathematics (M) and computer Science (C)
$\text{P}(\text{M}\cap\text{C})=\frac{1}{2}$
To find, $\text{P}\Big(\frac{\text{C}}{\text{M}}\Big)$
We know tht,
$\text{P}\Big(\frac{\text{C}}{\text{M}}\Big)=\frac{\text{P}(\text{M}\cap\text{C})}{\text{P(M)}}$
$=\frac{\frac{1}{2}}{\frac{4}{5}}$
$=\frac{1}{2}\times\frac{5}{4}$
$=\frac{8}{5}$
Required probability $=\frac{8}{5}$

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

Show that $\text{y}=\frac{\text{a}}{\text{x}}+\text{b}$ is a solution of the differential equation $\frac{\text{d}^2\text{y}}{\text{dx}^2}=\frac{2}{\text{x}}\Big(\frac{\text{dy}}{\text{dx}}\Big)=0$

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	$4$	$6$

If $\text{f}\text{(x)}=\begin{cases}\frac{1-\cos\text{x}}{\text {x}^2}, & \text{when} \text{ x}\neq 0\\1, & \text{when}\text{ x} = 0\end{cases}$ Show that f(x) is discontinuous at x = 0.

Differentiate the function $x^{x \cos x}+\frac{x^{2}+1}{x^{2}-1}$ w.r.t. x.

A total amount of ₹ $7000$ is deposited in three different saving bank accounts with annual interest rates $5\%, 8\%$ and $8\frac{1}{2}$% respectively. The total annual interest from these three accounts is ₹ $550$. Equal amounts have been deposited in the 5% and $8\%$ saving accounts. Find the amount deposited in each of the three accounts, with the help of matrices.

Evaluate the following integrals:
$\int\sin^3\sqrt{\text{x}}\text{dx}$

Find the particular solution of the differential equation $\frac{\text{dy}}{\text{d}x}=\frac{x(2\log x +1)}{\sin y+y\cos y}$given that $\text{y}=\frac{\pi}{2}\text{ when } x=1.$

If $\text{y}=\text{x}\sin^{-1}\text{x}+\sqrt{1-\text{x}^2},$ prove that $\frac{\text{dy}}{\text{dx}}=\sin^{-1}\text{x}$

Solve the following system of equations by matrix method:
$5x + 7y + 2 = 0$

$4x + 6y + 3 = 0$

Prove that $\frac{\text{dy}}{\text{dx}}\Big\{\frac{\text{x}}{2}\sqrt{\text{a}^2-\text{x}^2}+\frac{\text{a}^2}{2}\sin^{-1}\frac{\text{x}}{\text{a}}\Big\}=\sqrt{\text{a}^2-\text{x}^2}$