Download App

STD 11 - 14. probability — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 11 - 14. probability4 Marks
MCQ
The probability of $A, B, C$ solving a problem are $\frac{1}{3},\,\frac{2}{7},\,\frac{3}{8}$ respectively. If all the three try to solve the problem simultaneously, the probability that exactly one of them will solve it, is
  • A
    $\frac{{25}}{{168}}$
  • ✓
    $\frac{{25}}{{56}}$
  • C
    $\frac{{20}}{{168}}$
  • D
    $\frac{{30}}{{168}}$
✓

Answer

Correct option: B.
$\frac{{25}}{{56}}$
b
(b) Here ${p_1} = \frac{1}{3},$ ${p_2} = \frac{2}{7}$ and ${p_3} = \frac{3}{8}$

$ \Rightarrow {q_1} = \frac{2}{3},$ ${q_2} = \frac{5}{7}$ and ${q_3} = \frac{5}{8}$

Required probability $ = {p_1}{q_2}{q_3} - {q_1}{p_2}{q_3} + {q_1}{q_2}{p_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

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

The differential equation satisfied by the function $y = \sqrt {\sin x + \sqrt {\sin x + \sqrt {\sin x + .....\infty } } } $, is
→
The number of lines that are parallel to $2x + 6y + 7 = 0$ and have an intercept of length $10$ between the coordinate axes is
→
Number of solutions of $5$ $cos^2 \theta  -3 sin^2 \theta  + 6 sin \theta  cos \theta  = 7$ in the interval $[0, 2 \pi] $ is :-
→
If the probability of $X$ to fail in the examination is $0.3$ and that for $Y$ is $0.2$, then the probability that either $X$ or $Y$ fail in the examination is
→
Let $A(2, 3)$, $B(4, 5)$ and let $C$ = $(x, y)$ be a point such that $(x -2)(x -4) + (y -3)(y -5) = 0$. If area of .$\Delta ABC = \sqrt 2 $ sq. unit, then maximum number of positions of $C$ in the $xy$ plane is 
→
Let ${\left( { - \,2\, - \,\frac{1}{3}\,i} \right)^3} = \frac{{x \,+ \,iy}}{{27}}(i\, = \,\sqrt { - 1} ),$ where $x$ and $y$ are real numbers, then $y -x$ equals
→
If $a + b + c = 0$ and $p \ne 0,$ the lines $ax + (b + c)y = p,$ $bx + (c + a)y = p$ and $cx + (a + b)y = p$
→
The value of $\int\limits_{0}^{2\pi } {\left[ {\sin \,2x\left( {1 + \cos \,3x} \right)} \right]} \,dx$ where $[t]$ denotes the greatest integer function, is
→
How many words can be made out from the letters of the word $INDEPENDENCE$, in which vowels always come together
→
The remainder when $7^{2022}+3^{2022}$ is divided by 5 is.
→