Question

statistics probability tree diagrams practice worksheet - fall 2025
for problems 1 - 7 below:
a. draw and label the tree diagram that fits the given scenario.
b. calculate the probability of each branch, make sure they add to 1.

1. a basketball player shoots two free throws and has a 70% chance of making each shot. let x = the number of free throws made.

(x = 0)=0.09
(x = 1)=0.42
(x = 2)=0.49

1. a football team plays two games, they have an 80% chance of winning the first game, and a 40% chance of winning the second game. let x = the number of games won.

(x = 0)=0.12
(x = 1)=0.56
(x = 2)=0.32

1. a volleyball team plays three games and has a 60% chance of winning any game. let x = the number of games won.

(x = 0)=0.064
(x = 1)=0.288
(x = 2)=0.432
(x = 3)=0.216

1. a softball team plays a three - game series. they have a 40% chance of winning the first game, a 30% chance of winning the second, and a 75% chance of winning the third. let x = the number of games won.

Explanation:

Step1: Calculate P(X = 0) for softball team

The team loses all games. Probability of losing first game is $1 - 0.4=0.6$, second is $1 - 0.3 = 0.7$ and third is $1 - 0.75=0.25$. So $P(X = 0)=0.6\times0.7\times0.25 = 0.105$.

Step2: Calculate P(X = 1) for softball team

Three cases: Win - Lose - Lose: $0.4\times0.7\times0.25 = 0.07$; Lose - Win - Lose: $0.6\times0.3\times0.25= 0.045$; Lose - Lose - Win: $0.6\times0.7\times0.75 = 0.315$. Then $P(X = 1)=0.07 + 0.045+0.315 = 0.43$.

Step3: Calculate P(X = 2) for softball team

Three cases: Win - Win - Lose: $0.4\times0.3\times0.25 = 0.03$; Win - Lose - Win: $0.4\times0.7\times0.75=0.21$; Lose - Win - Win: $0.6\times0.3\times0.75 = 0.135$. Then $P(X = 2)=0.03+0.21 + 0.135=0.375$.

Step4: Calculate P(X = 3) for softball team

$P(X = 3)=0.4\times0.3\times0.75=0.09$.

Answer:

$P(X = 0)=0.105$, $P(X = 1)=0.43$, $P(X = 2)=0.375$, $P(X = 3)=0.09$