Q8 of 12 Page 13

In a game, a man wins ₹ 5 for getting a number greater than 4 and loses ₹ 1 otherwise, when a fair die is thrown. The man decided to throw a die thrice but to quit as and when he gets a number greater than 4. Find the expected value of the amount he wins/loses.

OR


A bag contains 4 balls. Two balls are drawn at random (without replacement) and are found to be white. What is the probability that all balls in the bag are white?[CBSE 2016]

Given: a man wins Rs. 5 for getting a number greater than 4 and loses Rs. 1 otherwise


To find: the expected value of the amount he wins/loses if he throws dice thrice


Let S be the success of getting number greater than 4 and F be the failure of getting number less than or equal to 4


As he quit as and when he gets a number greater than 4 i.e. S


Then sample space will be {S, FS, FFS, FFF}


Case 1: E1: gets success i.e. number greater than 4 on 1st throw



{∵ Favorable outcomes = {5, 6} = 2 &


Total outcomes = {1, 2, 3, 4, 5, 6} = 6}


He wins Rs 5


Case 2: E2: gets failure i.e. number less than or equal to 4 on 1st throw and gets success i.e. number greater than 4 on 2nd throw



He wins Rs 5 and loses Rs. 1


⇒ Amount = 5 – 1 = Rs. 4


Case 3: E3: gets failure 1st throw, gets failure on 2nd throw and gets success on 3rd throw



He wins Rs 5 and loses Rs. 2


⇒ Amount = 5 – 2 = Rs. 3


Case 4: E4: gets failure 1st throw, gets failure on 2nd throw and gets failure on 3rd throw



He loses Rs. 3


⇒ Amount = Rs. -3





Hence, expected value of prize he wins/loses, E(X),



OR


Given: A bag contains 4 balls


To find: probability that all balls in the bag are white


Formula used:


Bayes’ Theorem:


Given E1, E2, E3....En are mutually exclusive and exhaustive events, we can find the conditional probability P(Ei|A) for any event A associated with Ei as follows:



Two balls are drawn at random (without replacement) and are found to be white. This means at least two balls are white


Now,


Let A: Two drawn balls are white


E1: All the four balls are white


E2: Three balls are white


E3: Two balls are white


Since E1, E2, E3 are mutually exclusive and exhaustive events






Probability that all the balls are white is given by, P(E1|A)









Hence, probability that all balls in the bag are white is 0.6

More from this chapter

All 12 →
6

A bag X contains 4 while balls and 2 black balls, while another bag Y contains 3 white balls and 3 black balls. Two balls are drawn (without replacement) at random from one of the bags and were found to be one white and one black. Find the probability that the balls were drawn from bag Y.

OR


A and B throw a pair of dice alternately, till one of them gets a total of 10 and wins the game. Find their respective probabilities of winning, if A starts first.[CBSE 2016]

 7

There are two bags A and B. Bag A contains 3 white and 4 red balls whereas bag B contains 4 white and 3 red balls. Three balls are drawn at random (without replacement) from one of the bags and are found to be two white and one red. Find the probability that these were drawn from bag B.[CBSE 2016]

 9

Of the students in a school, it is known that 30% have 100% attendance and 70% students are irregular. Previous year results report that 70% of all students who have 100% attendance attain A grade and 10% irregular students attain A grade in their annual examination. At the end of the year, one student is chosen at random from the school and he was found to have an A grade. What is the probability that the student has 100% attendance? Is regularity required only in school? Justify your answer.[CBSE 2017]

 10

There are 4 cards numbered 1, 3 5 and 7, one number on one card. Two cards are drawn at random without replacement. Let X denote the sum of the numbers on the two drawn cards. Find the mean and variance of X.[CBSE 2017]