### UNIT - IX  Probability

1. Two fair dice are rolled. What is the probability that the sum on the faces of the two dice is 10?

Sol:  Trial: Dice are rolled

Sample Space:  { (1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6) (2, 1) (2, 2) (2, 3) (2, 4)

(2, 5) (2, 6) (3, 1 ) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6) (4, 1) (4, 2)

(4, 3) (4, 4) (4, 5) (4, 6) (5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6)

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

Total events :  36

Favourable events :  3

2. Find the probability that a non-leap year contains 53 sundays.

Sol: Non-leap year; 365 days

i.e . ,  52 weeks and 1 day

Sample Space:

{ Sun,  Mon,  Tue,  Wed,  Thu,  Fri,  Sat }

Total events :  7

Favourable events :  1

=  1/7

3. Find the probability that a non-leap year contains 52 Sundays only.

Sol: Non-leap year: 365 days

i.e., 52 weeks and 1 day

Sample space :

{ Sun,  Mon,  Tue,  Wed,  Thu,  Fri,  Sat }

Total Events :  7

Favourable events :  6

= 6/7

4. What is the probability that a leap year will contain 53 sundays ?

Sol:  Leap year :  366 days

i.e., 52 weeks and 2 days

Sample Space:

{ ( Sun,  Mon ), ( Mon,  Tue ),  ( Tue, Wed ),  ( Wed,  Thu ),  ( Thu,  Fri ),  ( Fri,  Sat )

( Sat,  Sun ) }

Total Events :  7

Favourable events :  2

Probability :  = 2/7

5. When 3 fair coins are tossed simultaneously find the probability to get at least one head.

Sol: Trial: Tossing 3 coins

Sample Space: { ( H H H ),  ( H H T ),  ( H T H ),  ( H T T ),  ( T T T ),  ( T T H ), ( T H T ),

( T H H ) }

Total events : 8

Favourable events to get at least one head : 7

Probability :  7/8

6. A talks the truth in 75% of the cases. B in 80% cases. What is the probability that their statements about an incident do not match ?

Sol: Probability of A that A talks the truth : P (A) = 75% =

Probability of A that A does not talk the truth  :

Probability of A that A does not talk the truth :

Probability of B that B talks the truth :

Probability that B does not talk the truth :

Probability of their statements about an incident donot match:

7. A, B, C are three horses in a race. The probability of A to win the race is twice that of B and probability of B is twice that of C. What are the probabilities of A, B, C to win the race ?

Sol: Given :  P (A)  =  2 P (B)

P (B)  =  2 P (C)

we know that P (A)  +  P (B)  +  P (C)  =  1

2 P (B)  +  P (B)  +  P (C)  =  1

3 P (B)  +  P (C)  =  1

3 [ 2 P (C) ]  +  P (C)  =  1

7 P (C)  =  1

P (C)  = 1/7

8. In a committee of 25 members, each member is expert in Mathematics (or) in Physics (or) in both. If 19 of these are expert in Mathematics, 16 in Physics find the probability that a person selected from the committee is expert in both.

Sol :  Total members :  25

Expert in Maths :  19

Expert in Physics :  16

9. A bag contains 12 two rupee coins, 7 one rupee coins and 4 half a rupee coins. If three coins are selected at random then find the probability that

(i)    The sum of the three coins is maximum.

(ii)    The sum of the three coins is minimum.

(iii)   Each coin is of different value.

Sol: Let E1 be the event that the sum of the three coins is maximum, E2 be the event that the sum of the three coins is minimum and E3 be the event that each coin is of different value.

Given: No.of two rupee coins : 12

No. of one rupee coins : 7

No. of half a rupee coins : 4

10. A bag B1 contains 4 white and 2 black balls. Bag B2 contains 3 white and 4 black balls. A bag is drawn at random and a ball is chosen at random from it. Then what is probability that the ball drawn is white ?

Sol: Let E1 be the event of selecting the bag B1 and E2 be the event of selecting the bag B2

Let E be the event of drawing a white ball from the selected bag

Posted Date : 26-11-2021

గమనిక : ప్రతిభ.ఈనాడు.నెట్‌లో కనిపించే వ్యాపార ప్రకటనలు వివిధ దేశాల్లోని వ్యాపారులు, సంస్థల నుంచి వస్తాయి. మరి కొన్ని ప్రకటనలు పాఠకుల అభిరుచి మేరకు కృత్రిమ మేధస్సు సాంకేతికత సాయంతో ప్రదర్శితమవుతుంటాయి. ఆ ప్రకటనల్లోని ఉత్పత్తులను లేదా సేవలను పాఠకులు స్వయంగా విచారించుకొని, జాగ్రత్తగా పరిశీలించి కొనుక్కోవాలి లేదా వినియోగించుకోవాలి. వాటి నాణ్యత లేదా లోపాలతో ఈనాడు యాజమాన్యానికి ఎలాంటి సంబంధం లేదు. ఈ విషయంలో ఉత్తర ప్రత్యుత్తరాలకు, ఈ-మెయిల్స్ కి, ఇంకా ఇతర రూపాల్లో సమాచార మార్పిడికి తావు లేదు. ఫిర్యాదులు స్వీకరించడం కుదరదు. పాఠకులు గమనించి, సహకరించాలని మనవి.

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