Download App

Probability — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsProbability3 Marks
Question
A die is thrown three times. Find $\text{P}\Big(\frac{\text{A}}{\text{B}}\Big)$ and $\text{P}\Big(\frac{\text{B}}{\text{A}}\Big)$, if
A = 4 appears on the third toss,
B = 6 and 5 appear respectively on first two tosses.
✓

Answer

Consider the given events.
A = Getting 4 on third throw
B = Getting 6 on first throw and and 5 on second throw
Clearly,
A = {(1, 1, 4), (1, 2, 4), (1, 3, 4), (1, 4, 4), (1, 5, 4), (1, 6, 4), (2, 1, 4), (2, 2, 4), (2, 3, 4), (2, 4, 4), (2, 5, 4), (2, 6, 4), ...... (6, 1, 4), (6, 2 4), (6, 3, 4), (6, 4, 4), (6, 5, 4), (6, 6, 4)}
B = {(6, 5, 1), (6, 5, 2), (6, 5, 3), (6, 5, 4), (6, 5, 5), (6, 5, 6)}
Now,
$(\text{A}\cap\text{B})=\{(6, 5, 4)\}$
$\therefore\ \text{Required probability} = \text{P}\Big(\frac{\text{A}}{\text{B}}\Big)=\frac{\text{n}(\text{A}\cap\text{B})}{\text{n}(\text{B})}=\frac{1}{6}$
$\therefore\ \text{Required probability} = \text{P}\Big(\frac{\text{B}}{\text{A}}\Big)=\frac{\text{n}(\text{A}\cap\text{B})}{\text{n}(\text{A})}=\frac{1}{36}$

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 "3 Marks Question" 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

Let A be any set containing more than one element. Let '*' be a binary operation on A defined by a * b = b for all a, b ∈ A. Is '*' commutative or associative on A?
→
For each of the differential equations in find a particular solution satisfying the given condition:
$\text{cos}\bigg(\frac{\text{dy}}{\text{dx}}\bigg) = \text{a}(\text{a} \in \text{R}); \ \text{y}=1\text{when x = }0$
→
Solve the following equation for x:
$\tan^{-1}\frac{\pi}{2}+\tan^{-1}\frac{\pi}{3}=\frac{\pi}{4},0<\text{x}<\sqrt6$
→
Find the equation of the line passing through the points (1, 2, -4) and parallel to the line $\frac{\text{x}-3}{4}=\frac{\text{y}-5}{2}=\frac{\text{z}+1}{3}.$
→
Evaluate the following definite integrals:
$\int_{1}^\limits{\text{e}}\frac{\text{e}^{\text{x}}}{\text{x}}(1+\text{x}\log\text{x})\text{dx}$
→
Verify Lagrange's mean value theorem for the following function on the indicated intervals. find a point 'c' in the indicated interval as stated by the Lagrange's mean value theorem.$\text{f}(\text{x})=\sin\text{x}-\sin2\text{x}-\text{x}\text{ on }[0,\pi]$
→
Let $R_0 $ denote the set of all non-zero real numbers and let $A = R_0 \times R_0.$ If '*' is a binary operation on adefined by,
$(a, b) * (c, d) = (ac, bd)$ for all $(a, b), (c, d) \in A$
Show that $'*'$ is both commutative and associative on $A.$
→
Find $f^{-1}$ if it exists: $f: A \rightarrow B$, where, $A=\{1,3,5,7,9\} ; B=\{0,1,9,25,49,81\}$ and $f(x)=x^2$.
→
A card is drawn at random from a well-shuffled pack of 52 cards. Find the probability that it is neither an ace nor a king.
→
Evaluate: $\int \frac{x+2}{\sqrt{x^2+2 x+3}}$
→