Ex 1. In a throw of a coin ,find the probability of getting a head. sol. Here s={H,T} and E={H}. P(E)=n(E)/n(S)=1/2

Ex2.Two unbiased coin are tossed .what is the probability of getting atmost one head? sol.Here S={HH,HT,TH,TT} Let Ee=event of getting one head E={TT,HT,TH} P(E)=n(E)/n(S)=3/4

Ex3.An unbiased die is tossed .find the probability of getting a multiple of 3 sol. Here S={1,2,3,4,5,6} Let E be the event of getting the multiple of 3 then ,E={3,6} P(E)=n(E)/n(S)=2/6=1/3

Ex4. In a simultaneous throw of pair of dice .find the probability of getting the total more than 7 sol. Here n(S)=(6*6)=36 let E=event of getting a total more than 7 ={(2,6),(3,5),(3,6),(4,4),(4,5),(4,6),(5,3),(5,4),(5,5),(5,6),(6,2),(6,3),(6,4),(6,5),(6,6)} P(E)=n(E)/n(S)=15/36=5/12.

Ex5. A bag contains 6 white and 4 black balls .2 balls are drawn at random. find the probability that they are of same colour. Sol .let S be the sample space Then n(S)=no of ways of drawing 2 balls out of (6+4)=^{10}c_{2}=(10*9)/(2*1)=45 Let E=event of getting both balls of same colour Then n(E)=no of ways(2 balls out of six) or(2 balls out of 4) =(^{6}c_{2}+^{4}c_{2})=(6*5)/(2*1)+(4*3)/(2*1)=15+6=21 P(E)=n(E)/n(S)=21/45=7/15

Ex6.Two dice are thrown together .What is the probability that the sum of the number on the two faces is divided by 4 or 6 sol. Clearly n(S)=6*6=36 Let E be the event that the sum of the numbers on the two faces is divided by 4 or 6.Then

Ex7.Two cards are drawn at random from a pack of 52 cards.what is the probability that either both are black or both are queen? sol. We have n(s)=^{52}c_{2}=(52*51)/(2*1)=1326. Let A=event of getting both black cards B=event of getting both queens A∩B=event of getting queen of black cards n(A)=^{26}c_{2}=(26*25)/(2*1)=325, n(B)=^{4}c_{2}=(4*3)/(2*1)=6 and n(A∩B)=^{2}c_{2}=1 P(A)=n(A)/n(S)=325/1326; P(B)=n(B)/n(S)=6/1326 and P(A∩B)=n(A∩B)/n(S)=1/1326 P(A∪B)=P(A)+P(B)-P(A∩B)=(325+6-1/1326)=330/1326=55/221

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Ex 1. In a throw of a coin ,find the probability of getting a head.sol. Here s={H,T} and E={H}.

P(E)=n(E)/n(S)=1/2

Ex2.Two unbiased coin are tossed .what is the probability of getting atmost one head?sol.Here S={HH,HT,TH,TT}

Let Ee=event of getting one head

E={TT,HT,TH}

P(E)=n(E)/n(S)=3/4

Ex3.An unbiased die is tossed .find the probability of getting a multiple of 3sol. Here S={1,2,3,4,5,6}

Let E be the event of getting the multiple of 3

then ,E={3,6}

P(E)=n(E)/n(S)=2/6=1/3

Ex4. In a simultaneous throw of pair of dice .find the probability of getting the total more than 7sol. Here n(S)=(6*6)=36

let E=event of getting a total more than 7

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

P(E)=n(E)/n(S)=15/36=5/12.

Ex5. A bag contains 6 white and 4 black balls .2 balls are drawn at random. find the probability that they are of same colour.Sol .let S be the sample space

Then n(S)=no of ways of drawing 2 balls out of (6+4)=

^{10}c_{2}=(10*9)/(2*1)=45Let E=event of getting both balls of same colour

Then n(E)=no of ways(2 balls out of six) or(2 balls out of 4)

=(

^{6}c_{2}+^{4}c_{2})=(6*5)/(2*1)+(4*3)/(2*1)=15+6=21P(E)=n(E)/n(S)=21/45=7/15

Ex6.Two dice are thrown together .What is the probability that the sum of the number on the two faces is divided by 4 or 6

sol. Clearly n(S)=6*6=36Let E be the event that the sum of the numbers on the two faces is divided by 4 or 6.Then

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

(6,6)}

n(E)=14.

Hence p(e)=n(e)/n(s)=14/36=7/18

Ex7.Two cards are drawn at random from a pack of 52 cards.what is the probability that either both are black or both are queen?

sol. We have n(s)=^{52}c_{2}=(52*51)/(2*1)=1326.Let A=event of getting both black cards

B=event of getting both queens

A∩B=event of getting queen of black cards

n(A)=

^{26}c_{2}=(26*25)/(2*1)=325,n(B)=

^{4}c_{2}=(4*3)/(2*1)=6 andn(A∩B)=

^{2}c_{2}=1P(A)=n(A)/n(S)=325/1326;

P(B)=n(B)/n(S)=6/1326 and

P(A∩B)=n(A∩B)/n(S)=1/1326

P(A∪B)=P(A)+P(B)-P(A∩B)=(325+6-1/1326)=330/1326=55/221