I already did the problems, but I just want to check if I\'m right. Can someone
ID: 3902292 • Letter: I
Question
I already did the problems, but I just want to check if I'm right. Can someone please confirm? Thanks!
Assume that the probability that the San Antonio Spurs wins a game over the Houston Rockets is 2/5 or 0.4.
a) What is the probability that the Rockets won the best of seven series over the Spurs in seven games? Answer: 0.166
6C3 = 20
chance of losing: 0.4
chance of winning: 1.0 - 0.4= 0.6
# of wins: 4/7 games
# of loses: 3/7 games
(20)(0.60)^4(0.40)^3 = 0.166
b) What is the probability that the Spurs won the series over the Rockets in 6 games? Answer: 0.207
5C3 = 10
chance of losing: 0.60
chance of winning: 0.40
# of wins: 4/6 games
# of loses: 2/6 games
(10)(0.40)^4(0.60)^2 = 0.207 probability
c) What is the probability that the Rockets won the series over the Spurs in 5 games? Answer. 0.207
4C3= 4
chance of losing: 0.4
chance of winning: 0.6
# of wins: 4/5 games
# of loses: 1/5 games
(4)(0.60)^4(0.4)= 0.207
d) What is the probability that the Spurs win the NBA championship? Answer: 0.7096
Explanation / Answer
Your logic is correct.
You have minor calculation error in problem b which I have corrected below.
Besides this you can explain you logic in words or some notation to make is easier to examine. By the way good answers correct logic.
Only question b is changed.
Answers:
1)
Final answer = Probability of Rockets winning 3 out of 6 first matches AND winning the last match
= (20)(0.60)^3(0.40)^3 * 0.6
= 0.276 * 0.6
= 0.1656
same for all sub problems.
b)
Final answer = Spurs winning 3 out of first 5 games * probability of Spurs winning the 6th game
= (10)(0.40)^3(0.60)^2 * 0.4
= 0.23 * 0.4
= 0.09216 ( Here you have calculation mistake in your answer)
c)
Final answer = Rockets winning 3 out of first 4 games * Rockets winning the 5th game
= (4)(0.60)^3(0.4) * 0.6
= 0.3456 * 0.6
= 0.20736
Yes, your method and answers are correct.
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