Go To Your Study Dashboard

Get Answers to all your Questions

header-bg

A man takes a step forward with probability $0.4$ and backward with probability $0.6$ . If the probability that at the end of eleven steps he is one step away from the starting point is $\lambda$ then the value of $5000 \lambda$ must be
Option: 1
$1580$

Option: 2
$1850$

Option: 3
$1058$

Option: 4
$5000$

Answers (1)

best_answer

Since, the man is one step away from starting point mean that either
(i) man has taken 6 steps forward and 5 steps backward.
(ii) man has taken 5 steps forward and 6 steps backward.
Taking, movement 1 step forward as success and 1 step backward as failure.

$\mathrm{\therefore \quad p=}$ probability of success $\mathrm{=0.4}$

and $\mathrm{q=}$ probability of failure $\mathrm{=0.6}$

$\mathrm{\therefore}$ Required probability $\mathrm{=P\{X=6 \: or \: X=5\}}$

$\mathrm{ =P(X=6)+P(X=5) }$

$\mathrm{ ={ }^{11} C_6 p^6 q^5+{ }^{11} C_5 p^5 q^6 }$

$\mathrm{ ={ }^{11} C_5\left(p^6 q^5+p^5 q^6\right) }$

$\mathrm{ =\frac{11 \cdot 10 \cdot 9 \cdot 8 \cdot 7}{1 \cdot 2 \cdot 3 \cdot 4 \cdot 5} \left\{(0.4)^6(0.6)^5+(0.4)^5(0.6)^6\right\} }$

$\mathrm{ =\frac{11 \cdot 10 \cdot 9 \cdot 8 \cdot 7}{1 \cdot 2 \cdot 3 \cdot 4 \cdot 5}(0.24)^5 }$

$\mathrm{ =0.37}$

Hence, the required probability $\mathrm{=0.37=\lambda}$ (given)

$\mathrm{\therefore 5000 \lambda =5000 \times 0.37 }$

$=1850$

Hence option 2 is correct.

Posted by

Ritika Jonwal

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

5 g of Na₂SO₄ was dissolved in x g of H₂O. The change in freezing point was found to be 3.82⁰C. If Na₂SO₄ is 81.5% ionised, the value of x (K

A capacitor is made of two square plates each of side 'a' making a very small angle $\alpha$

A solution of m-chloroaniline, m-chlorophenol and m-chlorobenzoic acid in ethyl acetate was extracted initially with a saturated solution of NaHCO₃ to give fraction A. The leftover organic phase was extracted with d

Trending Articles/News

anam-khan

JEE Main 2026 Registration LIVE: jeemain.nta.nic.in official website active; NTA clarifies typographical error

anam-khan

JEE Main 2026: IIT Delhi closing ranks for top BTech courses under open category

anam-khan

JEE Main 2026: NIT Trichy, Warangal among most competitive for ECE; remote NITs record higher closing ranks

Latest Question