probability

Question

 

India plays two matches each with West Indies and Australia. In any match, the probabilities of India getting, points 0, 1 and 2 are 0.45, 0.05 and 0.50 respectively. Assuming that the outcomes are independent, the probability of India getting at least 7 points is

Answer 1

Since there are 4 matches to be played.India can get a maximum of 8 points(2 points in each match).

Probability of getting exactly 7 points = P(Getting 2 points each of 3 matches and getting 1 point in one match)

=$\binom{4}{3}$ (0.5)³ (0.05)¹ =0.025

Probability of getting exactly 8 points =P(Getting 2 points in each of 4 matches)

=$\binom{4}{4}$ (0.5)⁴ (0.05)⁰=0.0625

P(india gets at least 7 points) =P(Getting exactly 7 points) + P(Probability of getting Exactly 8 points)

                                            = 0.025 + 0.0625

                                            =0.0875

Comments

atleast case can also be like that :

(43)pp(x=>7)=1-(probability of getting exactly 6 points)

=1-{ (434c3)(0.50)3 (0.45)1     } =0.775
but ans did not match correct me ??
 

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p(x=>7)=1-(probability of getting exactly 6 points)

This is wrong.

it should be p(x=>7)=1-(probability of getting at most 6 points) or 1-(probability of getting ' <7 ' points).

You have to consider all the cases.

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k got now..:) thanks..

Answer 2

Let if India loose gets point 0 Draws gets point 1 Wins gets point 2 
India will get point 7 if it wins 3 matches and Draws 1 
India will get point 8 if it wins all the 4 matches

Therefore combination of winning 3 matches 2 win with westindies and 1 win and 1 draw with australia  or vice versa 

.5*.5*.5*.05*4 = .025

Getting point 2 all win .5*.5*.5*.5 = .0625 

P(x>=7) = .025+ .0625 = .875
 

Comments

All the matches are different,

So there will be 4 possible cases in which India can score exactly 7 points.

Case 1, First Match against WI draw, Second match against WI and both matches against Australia won.

Case 2, Second Match against WI draw, First match against WI and both matches against Australia won.

Case 3, First Match against Australia draw, Second match against Australia and both matches against WI won.

Case 4, Second Match against Australia draw, First match against Australia and both matches against WI won.

So .5 *.5 * .5 *.05 * 4