Answer to Question #324269 in MatLAB for Shanu

Question

The “Titans” cricket team has a winning rate of 75%. The team is planning to play 10 matches in the next season.

 

a)    Let X be the number of matches that will be won by the team. What are the possible values of X?

b)    What is the probability that the team will win exactly 6 matches?

c)    What is the probability that the team will lose 2 or less matches?

d)    What is the mean number of matches that the team will win?

e)    What are the variance and the standard deviation of the number of matches that the team will win?

Answer 1

a) X may be any integer number from 0 to 10 inclusive

b) Let p=0.75 will be the probability to win a single match. Then the probability to win 6 matches and lose 4 in some concrete combination is p⁶ (1-p)⁴, but there ${10 \choose 6}$ such combinations. So the final answer is

$P ={10 \choose 6} p^6 (1-p)^4 = \frac{10!}{6! 4!} 0.75^6 0.25^4 \approx 0.14600$

c) The probability to lose 2 or fewer matches is equal to the sum of probabilities to win 8, 9, or 10 matches. So

$P ={10 \choose 8} p^8 (1-p)^2 + {10 \choose 9} p^9 (1-p) + {10 \choose 10} p^{10} = 45\cdot 0.75^8 \cdot0.25^2 + 10\cdot 0.75^9\cdot0.25 + 0.75^{10}\approx 0.52559$

d) The mean number of won matches is 10*p = 7.5

e) The variance of matches that the team will win is 10*p*(1-p) = 1.875, and the standard deviation is