Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • Let a dic be rolled n times. Let the probability of getting odd numbers seven times be equal to the probability of getting odd numbers nine times. If the probability of getting even numbers twice i

Let a dic be rolled n times. Let the probability of getting odd numbers seven times be equal to the probability of getting odd numbers nine times. If the probability of getting even numbers twice is \mathrm{\frac{k}{2^{15}}} , then k is equal to

Option: 1

60


Option: 2

30


Option: 3

90


Option: 4

15


Answers (1)

best_answer

$P($ odd \, \, number\, \, 7times $)=P($ odd \, \, number\, \, 9\, times $) $$

\begin{aligned} & { }^n C_7\left(\frac{1}{2}\right)^7\left(\frac{1}{2}\right)^{n-7}={ }^n C_9\left(\frac{1}{2}\right)^9\left(\frac{1}{2}\right)^{n-9} \\ & { }^n C_7={ }^n C_9 \\ & \Rightarrow n=16 \end{aligned}

Required

\begin{aligned} & P={ }^{16} C_2 \times\left(\frac{1}{2}\right)^{16} \\ & =\frac{16 \cdot 15}{2} \times \frac{1}{2^{16}}=\frac{15}{2^{13}} \\ & \Rightarrow \frac{60}{2^{15}} \Rightarrow k=60 \end{aligned}

Posted by

Gaurav

View full answer

JEE Main high-scoring chapters and topics

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

Similar Questions

Trending Articles/News

anam-khan

JEE Main 2025: BTech ECE cut-offs for female candidates go up at top NITs
anam-khan

JEE Main 2025 Session 2 City Slip (OUT) Live: Admit card likely on March 29 at jeemain.nta.nic.in; cut-offs
anam-khan

AESL expands Aakash Digital 2.0 to offer AI-powered coaching for NEET, JEE, Olympiads

Latest Question