Download Lab 6-5 Situation #1

Lab 6-5 Situation #1
On each point in tennis, a player is allowed two tries to successfully serve the ball into
the service box of the opponent’s side of the court. If the player is not successful in
these two tries, the player automatically loses the point. This is called a double fault.
Suppose while playing in a tournament, a certain professional player gets his first serve
in the service box about 75% of the time. When he gets his first serve in, he wins the
point about 80% of the time. If he misses his first serve, his second serve goes in the
service box about 90% of the time. When this happens, he wins the point on the second
serve about 40% of the time.
a) Draw a tree diagram of all the possible outcomes.
Determine each of the following probabilities:
a) P(misses the first serve)
b) P(wins the point | first serve in)
c) P(loses the point | first serve in)
d) P(first serve in and wins the point)
e) P(second serve in | first serve misses)
f) P(misses second serve)
g) P(win the point | second serve in)
h) P(lose the point | second serve in)
i) P(first serve out and second serve in and win the point)
j) P(wins the point)
Lab 6-5 Situation #1
On each point in tennis, a player is allowed two tries to successfully serve the ball into
the service box of the opponent’s side of the court. If the player is not successful in
these two tries, the player automatically loses the point. This is called a double fault.
Suppose while playing in a tournament, a certain professional player gets his first serve
in the service box about 75% of the time. When he gets his first serve in, he wins the
point about 80% of the time. If he misses his first serve, his second serve goes in the
service box about 90% of the time. When this happens, he wins the point on the second
serve about 40% of the time.
a) Draw a tree diagram of all the possible outcomes.
.8
W
I
W
0.6
.75
.2
1st
.25
I – In
O – Out
I
.9
L
2nd
W
.6
L
0.15
0I
00
0.135
0.025
0.09
I
0
.1
.4
I
L
Results
0I
W
0
L
L
Determine each of the following probabilities:
a) P(misses the first serve)
0.25
b) P(wins the point | first serve in)
0.8
c) P(loses the point | first serve in)
0.2
d) P(first serve in and wins the point)
0.75  0.8 = 0.6
e) P(second serve in | first serve misses)
f) P(misses second serve)
0.9
0.1
g) P(win the point | second serve in)
0.4
h) P(lose the point | second serve in)
0.6
i) P(first serve out and second serve in and win the point)
j) P(wins the point)
0.6 + 0.09 = 0.69
0.25  0.9  0.4 = 0.09
LAB 6-5 Situation # 2
Suppose the local weather station has collected and analyzed data about the probability of
precipitation in your region. The results predict that if it rains on one day, then the chance
it will rain on the next day is 50%. If it is not raining, it will rain on the next day only 20% of
the time.
a) Is the statement “If it rains on one day, then the chance it will rain on the next day is
50%, a conditional probability? Explain
b) Determine P(does not rain next day | rains today)
c) If it does not rain today, what is the probability that it will rain the next day?
d) Determine P(does not rain the next day | does not rain today)
e) The weather forecast for today predicts a 90% chance of rain. Starting with today as
the first day, the following tree diagram gives the sample space for three consecutive
days of weather outcomes. Each branch of the tree indicates whether it rains (R) or
does not rain (N). Complete the tree diagram.
1St Day
2nd Day
3rd Day
R
___
Outcomes
RRR
___
N
___
___
___
___
R
___
___
___
___
N
___
___
___
___
R
R
N
f) Determine the probability that it rains on all three days
g) Determine the probability that it rains only on the third day
h) Determine the probability that it rains on the third day
i) You are given that it rains on the first day. What is the probability that it rains on the
third day?
LAB 6-5 Situation # 3
Suppose your high school basketball team is playing in a best-of-three (win two games)
holiday tournament against another local team.
a) Construct a tree diagram to determine the sample space for this situation
b) The coach feels the team has a 50-50 chance of winning the first game against the very
strong opponent. If the team wins the game, the probability of winning the next game
increases to 2/3. If the team loses the game, the probability of winning the next game is
1/3.
1) If the team wins the game, what is the probability of losing the next game?
2) If the team loses the game, what is the probability of losing the next game?
c) What is the probability that the team wins the first game, but loses the next two games?
d) What is the probability that the team wins the first two games?
e) What is the probability that the team wins the tournament, given it wins the first game?
f) What is the probability that the team wins the tournament?