Question

A coach has found that his team wins about 4/5 of their home games.

To be in the playoffs, the team must win 3 or more of its next 4 home games. To estimate the probability of this happening, the coach uses a computer to randomly select 4 numbers from 1 through 5. He lets 1 through 4 represent winning and 5 represent losing.

He repeats this for a total of 20 trials and records the results in the table below.

of their home games.

To be in the playoffs, the team must win 3 or more of its next 4 home games. To estimate the probability of this happening, the coach uses a computer to randomly select 4 numbers from 1 through 5. He lets 1 through 4 represent winning and 5 represent losing.

He repeats this for a total of 20 trials and records the results in the table below.

What is the best estimate, based on this simulation, of the probability the team will win 3 or more of their next 4 home games?

(a) 5%

(b) 35%

(c) 65%

(d) 95%

Answer 1

it is a 95% chance if they win 4/5 of there home games and they have to win 3 or more then they will mostly will when the 3 of the games they need.

Answer 2

The best estimate of the probability of winning 3 or more games is:

95%.

Explanation:

To be in the playoffs, the team must win 3 or more of its next 4 home games.

The coach uses a computer to randomly select 4 numbers from 1 through 5. He lets 1 through 4 represent winning and 5 represent losing.

The table of values that represent his trials are:

4125 4324 4431 2254 3124 4421 2254 1322 5254 3213 5444 3213 3234 3322 5322 4341 1315 1241 4241 1335.

Hence, total number of trials=20

Outcomes in which the team will win 3 or more of their home games is:

4125 4324 4431 2254 3124 4421 2254 1322 3213 5444 3213 3234 3322 5322 4341 1315 1241 4241 1335.

Hence, number of outcomes in which they win 3 or more games=19.

Hence, the best estimate of the probability the team will win 3 or more of their next 4 home games is:

`=(19)/(20)* 100\\\\\\=95\%`

Hence, the probability is:

95%