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Question64 college basketball teams are split into 4 regions. Find the sample space size, teams in West (WW), and P(W)P(W).
Answer: There are 6464 teams in the sample space. There are 1616 teams in the event WW. P(W)=14P(W)=\frac{1}{4}.

Studdy Solution

STEP 1

Assumptions1. The total number of teams is64. . The teams are divided equally into four regions West, South, East, and North.
3. Let WW be the event that a team is assigned to the West region.

STEP 2

First, we need to find the total number of teams in the sample space. This is given by the total number of teams, which is64.
Total number of teams in the sample space=64\text{Total number of teams in the sample space} =64

STEP 3

Next, we need to find the number of teams in the event WW. Since the teams are divided equally into four regions, we can find this by dividing the total number of teams by.
Number of teams in event W=Total number of teams\text{Number of teams in event } W = \frac{\text{Total number of teams}}{}

STEP 4

Plug in the given value for the total number of teams to calculate the number of teams in event WW.
Number of teams in event W=644\text{Number of teams in event } W = \frac{64}{4}

STEP 5

Calculate the number of teams in event WW.
Number of teams in event W=644=16\text{Number of teams in event } W = \frac{64}{4} =16

STEP 6

Now, we need to find the probability that a randomly chosen team is in event WW. This is given by the ratio of the number of teams in event WW to the total number of teams.
(W)=Number of teams in event WTotal number of teams(W) = \frac{\text{Number of teams in event } W}{\text{Total number of teams}}

STEP 7

Plug in the values for the number of teams in event WW and the total number of teams to calculate the probability.
(W)=1664(W) = \frac{16}{64}

STEP 8

Calculate the probability that a randomly chosen team is in event WW.
(W)=1664=0.25(W) = \frac{16}{64} =0.25So, the answers areThere are64 teams in the sample space. There are16 teams in the event WW. (W)=0.25(W)=0.25, is the probability that a randomly chosen team is in event WW.

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