SATHEE: Probability 5 Question 11

Probability 5 Question 11

11. One hundred identical coins, each with probability $p$ , of showing up 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, then the value of $p$ is

(1988, 2M)

(a) $1 / 2$

(b) $49 / 101$

(d) $51 / 101$

Fill in the Blanks

Show Answer

Answer:

Correct Answer: 11. (d)

Solution:

Let $X$ be the number of coins showing heads. Let $X$ be a binomial variate with parameters $n = 100$ and $p$ .

Since,

$P (X = 50) = P (X = 51)$

$\begin{aligned} \Rightarrow & ^{100} C_{50} p^{50} (1 - p)^{50} & =^{100} C_{51} (p)^{51} (1 - p)^{49} \\ \Rightarrow & \frac{(100)!}{(50!) (50!)} \cdot \frac{(51!) \times (49!)}{100!} & = \frac{p}{1 - p} \Rightarrow \frac{p}{1 - p} = \frac{51}{50} \\ \Rightarrow & p & = \frac{51}{101} \end{aligned}$

पिछला

अगला

गोपनीयता नीति

द्वारा संचालित Prutor@IITK

sathee@iitk.ac.in

SATHEE का मीडिया कवरेज

खेल स्टोर

ऐप स्टोर

Ask SATHEE

Welcome to SATHEE !
Select from 'Menu' to explore our services, or ask SATHEE to get started. Let's embark on this journey of growth together! 🌐📚🚀🎓

I'm relatively new and can sometimes make mistakes.
If you notice any error, such as an incorrect solution, please use the thumbs down icon to aid my learning.
To begin your journey now, click on "I understand".

Probability 5 Question 11

11. One hundred identical coins, each with probability p, of showing up 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, then the value of p is

Fill in the Blanks

Answer:

इंजीनियरिंग की तैयारी

चिकित्सा तैयारी

एनसीईआरटी पुस्तकें और समाधान

महत्वपूर्ण संसाधन

अन्य संसाधन

पाठ्यक्रम

परीक्षा मंच

नमूना मॉक टेस्ट

सदस्यता

एनसीईआरटी व्यायाम वीडियो समाधान

Menu

11. One hundred identical coins, each with probability $p$ , of showing up 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, then the value of $p$ is