Download App

Probability — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsProbability2 Marks
Question
If $\mathrm{P}\left(\mathrm{A}^{\prime}\right)=0.7, \mathrm{P}(\mathrm{B})=0.7, \mathrm{P}(\mathrm{B} / \mathrm{A})=$ 0.5 , find $\mathrm{P}(\mathrm{A} / \mathrm{B})$ and $\mathrm{P}(\mathrm{A} \cup \mathrm{B})$.
✓

Answer

Since $1-P\left(A^{\prime}\right)=0.7$
$
\mathrm{P}(\mathrm{A})=1-\mathrm{P}\left(\mathrm{A}^{\prime}\right)=1-0.7=0.3
$
Now $\mathrm{P}(\mathrm{B} / \mathrm{A})=\mathrm{P}(\mathrm{A} \cap \mathrm{B}) / \mathrm{P}(\mathrm{A})$
$
\therefore 0.5=\mathrm{P}(\mathrm{A} \cap \mathrm{B}) / 0.3
$
$\therefore \mathrm{P}(\mathrm{A} \cap \mathrm{B})=0.15$
Again $\mathrm{P}(\mathrm{A} / \mathrm{B})=\mathrm{P}(\mathrm{A} \cap \mathrm{B}) / \mathrm{P}(\mathrm{B})$
$=0.15 / 0.7$
$\therefore \mathrm{P}(\mathrm{A} / \mathrm{B})=3 / 14$
Further, by addition theorem
$
\begin{aligned}
& P(A \cup B)=P(A)+P(B)-P(A \cap B) \\
& =0.3+0.7-0.15=0.85
\end{aligned}
$

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 "Solve the Following Question.(2 Marks)" from Probability→Probability — all question types→Maths STD 11 Science question papers→Maharashtra Board STD 11 Science question papers→Maharashtra Board question paper generator→

Similar questions

Write the relation in the Roster form. State its domain and range.

$R_6=\{(a, b) / a \in N, a<6$ and $b=4\}$

→
Show the following quadratic equation by factorization method:
$x^2 - x + 1 = 0$
→
From a group of 15 cricket players, a team of 11 players is to be chosen. In how many ways can this be done?
→
Find the equation of a circle with centre at $(-3, -2)$ and radius $6.$
→
How many 4 letter words can be formed using letters in the word MADHURI, if (a) letters can be repeated (b) letters cannot be repeated.
→
Which term of the progression $0.004, 0.02, 0.1, ...$ is $12.5 ₹$
→
The vertices of a triangle are A(3, 4), B(2, 0) and C(- 1, 6). Find the equations of the lines containing. : the midpoints of sides AB and BC.
→
Prove that:
$\sec\Big(\frac{3\pi}{2}-\text{x}\Big)\sec\Big(\text{x}-\frac{5\pi}{2}\Big)+\tan\Big(\frac{5\pi}{2}+\text{x}\Big)\tan\Big(\text{x}-\frac{3\pi}{2}\Big)=-1$
→
Find the centre and radius of the circle x = 3 – 4 sin θ, y = 2 – 4 cos θ.
→
Solve the following quadratic equations:

$x^2-4 x+13=0$

→