Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • Try this! One hundred identical coins, each with probability p of showing heads are tossed once. If 0 < p < 1 and the probability of heads showing on 50 coins is equal to that of heads showing on 51 coins, the value of p is

One hundred identical coins, each with probability p of showing heads are tossed once. If 0 < p < 1 and the probability of heads showing on 50 coins is equal to that of heads showing on 51 coins, the value of p is

  • Option 1)

    \frac{1}{2}

     

     

  • Option 2)

    \frac{51}{101}

  • Option 3)

    \frac{49}{101}

  • Option 4)

    none of these

 

Answers (1)

best_answer

As we learned

 

Binomial Theorem on Probability -

Then

\dpi{100} P\left ( X= r \right )     or   P(r)

=\ ^{n}C_{\Upsilon }\cdot P^{r }\cdot q^{n-r}

-

 

 Let X be the number of coins showing heads.

Then X follows a binomial distribution with parameters n = 100 and p.

since P(X=50)=P(X=51) , we get, ^{100}C_(50)p^{50}(1-p)^{50}=^{100}C_{51}p^{51}(1-p)^{49}

\Rightarrow \frac{100!}{50!50!}\cdot \frac{51!49!}{100!}=\frac{p}{1-p}\Rightarrow \frac{51}{50}=\frac{p}{1-p}\Rightarrow 51-51p=50p\Rightarrow p=\frac{51}{101}

 


Option 1)

\frac{1}{2}

 

 

Option 2)

\frac{51}{101}

Option 3)

\frac{49}{101}

Option 4)

none of these

Posted by

Himanshu

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 2024 Topper: Farmer’s son Gajare Nilkrishna says ‘keep questioning until you understand’
anam-khan

NIT Puducherry Cut-off 2024: Computer Science and Engineering had highest closing rank last year
anam-khan

What after JEE Main results 2024? All you need to know about JEE Adv, CSAB, JoSAA counselling

Latest Question