Question

does the colorado avalanche nhl hockey team perform differently in games that go into overtime (or shootout) compared to games that dont? the table shows data for the colorado avalanche over six seasons.

season	games played	total wins	overtime or shootout games played	wins in overtime or shootout games
2021-22	82	56	14	12
2020-21	56	39	16	9
2019-20	70	42	17	9
2018-19	82	38	16	2
2017-18	82	43	18	9
total	454	269	95	46

let a represent the event \the avalanche wins a game\ and b represent \the game goes to overtime or shootout\.

1. use the data to estimate the probabilities. explain or show your reasoning.

a. ( p(a) )

b. ( p(b) )

c. ( p(a \text{ and } b) )

d. ( p(a|b) )

Explanation:

1a. \( P(A) \)

Step1: Recall probability formula

Probability of an event \( A \) is \( P(A)=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \). For \( P(A) \), favorable outcomes are total wins, total outcomes are total games played.

Step2: Identify values

Total wins (favorable for \( A \)) = 269, Total games played = 454.

Step3: Calculate \( P(A) \)

\( P(A)=\frac{269}{454}\approx0.5925 \)

1b. \( P(B) \)

Step1: Recall probability formula

\( P(B)=\frac{\text{Number of games in overtime/shootout}}{\text{Total games played}} \).

Step2: Identify values

Games in overtime/shootout = 95, Total games played = 454.

Step3: Calculate \( P(B) \)

\( P(B)=\frac{95}{454}\approx0.2092 \)

1c. \( P(A \text{ and } B) \)

Step1: Recall probability formula

\( P(A \text{ and } B)=\frac{\text{Wins in overtime/shootout}}{\text{Total games played}} \).

Step2: Identify values

Wins in overtime/shootout = 46, Total games played = 454.

Step3: Calculate \( P(A \text{ and } B) \)

\( P(A \text{ and } B)=\frac{46}{454}\approx0.1013 \)

1d. \( P(A|B) \)

Answer:

s:
a. \( \boldsymbol{\frac{269}{454}\approx0.593} \) (or exact fraction \( \frac{269}{454} \))
b. \( \boldsymbol{\frac{95}{454}\approx0.209} \) (or exact fraction \( \frac{95}{454} \))
c. \( \boldsymbol{\frac{46}{454}\approx0.101} \) (or exact fraction \( \frac{23}{227} \))
d. \( \boldsymbol{\frac{46}{95}\approx0.484} \) (or exact fraction \( \frac{46}{95} \))