Q34 of 249 Page 32

Out of 100 students, two sections of 40 and 60 are formed. If you and your friend are among 100 students, what is the probability that: (i) you both enter the same section? (ii) you both enter the different section?

Given:


Section A contains 40 students


Section B contains 60 students


It is told that you and your friend are among 100 students


We need to find:


i. You both enter the same section


ii. You both enter the different section


⇒ P(Ssame) = P(You and your friend enter same section)


This happens only in the case if you and your friend belongs to either section A or section B.


⇒ P(Ssame) = P(Both belongs to section A) + P(Both belongs to section B)


⇒


⇒


⇒


⇒


⇒


⇒


⇒ P(Sdiff) = P(You and your friend enter different section)


This happens only in the case if you belongs to A and your friend belongs to section B.


⇒ P(Sdiff) = 1-P(Both belongs to same section)


⇒ P(Sdiff) = 1-P(Ssame)


⇒


⇒


∴ The required probabilities are .


More from this chapter

All 249 →
32

An urn contains 7 red and 4 blue balls. Two balls are drawn at random with replacement. Find the probability of getting.

i. 2 red balls


ii. 2 blue balls


iii. One red and one blue ball

 33

A card is drawn from a deck of 52 cards. The outcome is noted, the card is replaced and the deck reshuffled. Another card is then drawn from the deck.

i. What is the probability that both the cards are of the same suit?


ii. What is the probability that the first card is an ace and the second card is a red queen?

 35

In a hockey match, both teams A and B scored same number of goals up to the end of the game, so to decide the winner, the referee asked both the captains throw a die alternately and decide that the team, whose captain gets a first six, will be declared the winner. If the captain of team A was asked to start, find their respective probabilities of winning the match and state whether the decision of the referee was fair or not.

 36

A and B throw a pair of die alternately. A wins the game if he gets a total of 7 and B wins the game if he gets a total of 10. If A starts the game, then find the probability that B wins.