Problem Solving

Team A plays two matches each with Team B and Team C. In any match, the probability of different outcome for Team A is given below:

Outcome Win / Loss / Draw


Probability 0.5 / 0.45 / 0.05


Points 2 / 0 / 1

Outcome of all the matches are independent of each other.

Q1: What is the probability of Team A getting at least 7 points in the contest? Assume Team B and Team C play 2 matches.
A. 0.025
B. 0.0875
C. 0.0625
D. 0.975
E None of these

Q2. What is the probability of Team C getting at least 4 points? Assume Team C and Team B play 2 matches.

A. 0.2025
B. 0.0625
C. 0.0425
D. 0.050
E. Can't be determined

My Doubts:

In question 1 the statement "Assume Team B and Team C play 2 matches" what information is this statement providing.

In question 2: "Assume Team C and Team B play 2 matches" is it not conflicting with the information in the us. Moreover the table only shows the probability of win or lose for Team A. So can I say it can't be determined?

My Solution Approach:

For Team A to have at least 7 points, out of total 4 matches that it plays with Team B and Team C. It should either Win 3 and draw 1 or Win all of them.

So the first case of winning all matches:

W X W X W X W = 0.5 X 0.5 X 0.5 X 0.5 = 0.0625

Second case, Winning 3 draw 1:

W X W X W X D = 0.5 X 0.5 X 0.5 X 0.05 = .00625 x 4 = .025 (as it is possible in following 4 ways)

W W W D
W W D W
W D W W
D W W W

So probability of getting at least 7 points = .025 + .0625 = 0.0875

Answer B;

Solution 2:

Can't determine as there is no information for the probability of outcome for the match between B & C. Is it correct?

Please advise. Thank you.