There are 10 coins in a box, out of which 8 a | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Let $E_1$ be the event of choosing a fair coin and $E_2$ be the event of choosing a two-headed coin. $P(E_1) = \frac{8}{10} = \frac{4}{5}$ and $P(

Vedclass · Accepted Answer

$\frac{16}{17}$

Vedclass · Answer

(A) Let $E_1$ be the event of choosing a fair coin and $E_2$ be the event of choosing a two-headed coin. $P(E_1) = \frac{8}{10} = \frac{4}{5}$ and $P(E_2) = \frac{2}{10} = \frac{1}{5}$. Let $A$ be the event that the coin shows heads $6$ times in $6$ tosses. $P(A|E_1) = (\frac{1}{2})^6 = \frac{1}{64}$. $P(A|E_2) = 1^6 = 1$. Using Bayes' Theorem, the probability that the selected coin is two-headed given that it showed heads $6$ times is: $P(E_2|A) = \frac{P(E_2) 	imes P(A|E_2)}{P(E_1) 	imes P(A|E_1) + P(E_2) 	imes P(A|E_2)}$. $P(E_2|A) = \frac{\frac{1}{5} 	imes 1}{\frac{4}{5} 	imes \frac{1}{64} + \frac{1}{5} 	imes 1} = \frac{\frac{1}{5}}{\frac{1}{80} + \frac{1}{5}} = \frac{\frac{1}{5}}{\frac{1+16}{80}} = \frac{1}{5} 	imes \frac{80}{17} = \frac{16}{17}$.

There are $10$ coins in a box, out of which $8$ are normal and the remaining are with heads on both sides. $A$ coin is chosen at random from the box and tossed $6$ times. If it shows heads each time, then the probability that the selected coin has heads on both sides is

Similar Questions

$A$ card from a pack of $52$ cards is lost. From the remaining $51$ cards,$n$ cards are drawn and are found to be spades. If the probability of the lost card being a spade is $\frac{11}{50}$,then $n$ is equal to

In an entrance test,there are multiple-choice questions. There are four possible answers to each question,of which one is correct. The probability that a student knows the answer to a question is $9/10$. If he gets the correct answer to a question,then the probability that he was guessing is:

$A$ pack of playing cards was found to contain only $51$ cards. If the first $13$ cards which are examined are all red,then the probability that the missing card is black,is

The probabilities of having a defective toy in three cartons $A, B, C$ are $\frac{1}{3}, \frac{1}{4}, \frac{2}{5}$ respectively. If a carton is selected at random and a toy drawn randomly from it is found to be defective,then the probability that it is drawn from carton $B$ is

$A$ bag contains $6$ balls. Two balls are drawn from it at random and both are found to be black. The probability that the bag contains at least $5$ black balls is

Vedclass Test Series

Exam Paper Generator

Online Exam Module