# PROBABILITY SOLUTIONS Question & Answers

## PROBABILITY SOLUTIONS Question & Answers

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## PROBABILITY SOLUTIONS Question & Answers

Experiment  An event which can give some well-defined outcomes is called an experiment.

Random Experiment:  An experiment in which all possible outcomes are known in advance and the exact output cannot be defined in advance is called a random experiment. Eg:

1) Rolling an unbiased dice.

2) Tossing a fair coin.

3) Drawing a card randomly from a pack of well-shuffled cards.

Note:

• When we throw a coin, then there are two possibilities either a Head(H) or a Tail(T) will appear.
• A dice is a solid cube having 6 faces, marked as 1,2,3,4,5,6 respectively. When we throw a die randomly, the outcome is the number from one among them that appears on its upper face.
• A pack of cards has 52 cards.It has 13 cards of each suit, namely spades, clubs, hearts, and diamonds. Cards of spades and clubs are black in color that’s why are black cards.Cards of hearts and diamonds are red in color that’s why are red cards.
• There are four honors in each suit.These are Aces, Kings, Queens and Jacks.These are also known as Face cards.

Sample Space: When we perform an experiment, then the set S of all possible outcomes is called the Sample space of that experiment. E.g:

1) While tossing one coin S= {H,T}.

2)If two coins are tossed simultaneously, then S= {HH,HT,TH,TT}.

3) While throwing a dice, we have S={1,2,3,4,5,6}.

Event: Any subset formed from a sample space is called an Event.

The probability of occurrence of an Event:

Let S be the sample space & E be the Event. Then,

Probability of E p(E) =n(E)/n(S).

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Important Results on Probability:

1)P(S) =1.

2) 0 <P(E) < 1 (probability of an occurrence of event always lie between 0 and 1).

3) Max value of probability of an event is one.

4) For any events A and B we have:

P(AUB) =P(A) +P(B) -P(AnB).

Eg:1 An unbiased die is rolled. Find the probability of getting a number that is a multiple of 3?

Sol: Here In this problem we have sample space S={1,2,3,4,5,6}.

Let E be the event of getting a number that is multiple of 3.

Then E={3,6}.

P(E) =n(E)/n(S).

n(E) =2,  n(S) =6.

P(E) =2/6

P(E) =1/3.

Eg: 2 In we simultaneously throw a pair of dice together, then find the probability of getting a total more than 7or more on the upper faces of the dice?

Sol: Here we have sample space n(S) =6*6 =36.

Let E be the event of getting a total more than 7.

={(1,6),(2,5),(3,4),(4,3)(5,2),(6,1)(2,6),(3,5),(4,4),(5,3),(6,2),(4,5),(5,4),(5,5),(4,6),(6,4)}

n(E) =15

P(E) = n(E)/n(S)

= 15/36.

P(E) = 5/12.

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August 25, 2019