Suppose that the SJCS and Mary Ward are in the basketball final. In this best-of-three series, the winner is the first team to win two games. There are 60% chances SJCS TEAM will win first game. If SJCS wins, there are a 70% chance of winning next game and if they lose there are 45% chances of winning next game.
Create a tree diagram and find the probability for each case
Find the probability of SJCS win the series
I really don't understand how to draw the diagram... And finding the probability of them winning. Please help
Not possible to show tree diagram here, but I would start a tree for each school
with two branches whose endpoints would be W and L (for win and lose)
From the W end, I need two more branches, again labeled W and L
Do the same for the L end, etc until a series of branches has 2 W's
Suppose we look at the SJCS branches
they can win along the following branches:
WW -->(.6)(.7) = .42
WLW --> (.6)(.3)(.45) = .081
LWW --> (.4)(.45)(.7) = .126
prob(SJCS wins) = .42 + .081 + .126 = .627
To create the tree diagram and find the probabilities, follow these steps:
Step 1: Start by drawing a horizontal line to represent the start of the series.
Step 2: On the left side of the line, write "SJCS Wins Game 1" and draw an arrow pointing to a branch below.
Step 3: On the right side of the line, write "SJCS Loses Game 1" and draw an arrow pointing to another branch below.
Step 4: From the branch below "SJCS Wins Game 1," draw two branches. On the left branch, write "SJCS Wins Game 2" and on the right branch, write "SJCS Loses Game 2".
Step 5: From the branch below "SJCS Loses Game 1," draw two branches. On the left branch, write "SJCS Wins Game 2" and on the right branch, write "SJCS Loses Game 2".
Step 6: From each "Game 2" branch, draw two final branches. On the left branch, write "SJCS Wins Series" and on the right branch, write "SJCS Loses Series".
Step 7: Assign probabilities to each branch based on the given information.
- There is a 60% chance that SJCS wins Game 1, so assign a probability of 0.6 to the branch "SJCS Wins Game 1" and 0.4 to the branch "SJCS Loses Game 1".
- If SJCS wins Game 1, there is a 70% chance they win Game 2. Assign a probability of 0.7 to the branch "SJCS Wins Game 2" (from "SJCS Wins Game 1") and 0.3 to the branch "SJCS Loses Game 2" (from "SJCS Wins Game 1").
- If SJCS loses Game 1, there is a 45% chance they win Game 2. Assign a probability of 0.45 to the branch "SJCS Wins Game 2" (from "SJCS Loses Game 1") and 0.55 to the branch "SJCS Loses Game 2" (from "SJCS Loses Game 1").
- Finally, assign a probability of 1 to "SJCS Wins Series" and 0 to "SJCS Loses Series" (from both "SJCS Wins Game 2" and "SJCS Loses Game 2").
Step 8: Calculate the probabilities for each case by multiplying the probabilities along the corresponding branches.
- Probability of SJCS winning Game 1 and Game 2: 0.6 * 0.7 = 0.42
- Probability of SJCS winning Game 1 and losing Game 2: 0.6 * 0.3 = 0.18
- Probability of SJCS losing Game 1 and winning Game 2: 0.4 * 0.45 = 0.18
- Probability of SJCS losing Game 1 and losing Game 2: 0.4 * 0.55 = 0.22
Step 9: Calculate the probability of SJCS winning the series by adding up the probabilities of all the cases where they win. In this case, it is the probability of SJCS winning Game 1 and Game 2, which is 0.42.
Therefore, the probability of SJCS winning the series is 0.42 (or 42%).