The table shows the number of championships won by the baseball and softball leagues of three youth baseball divisions organized by age groups.
baseball league (b) softball league (s)
ages 7 – 9 (x) 3 7
ages 10 – 12 (y) 2 2
ages 13 – 15 (z) 1 1
question 1:
if the winning team plays in the ages 10 - 12 division, find the probability that the team is in the baseball league. answer in terms of a reduced fraction.
p(b|y) =
question 2:
if the winner is in baseball league, find the probability that the winning team is in either the ages 10 - 12 division or the ages 13 - 15 division. answer in terms of a reduced fraction. (this is a three part question)
a. p(y | b) =
b. p(z | b) =
c. p(y or z |b) =
answer all of these questions. good luck!

Question 1:

Question 2:

A.

B.

C.

Step-by-step explanation:

Conditional probability is defined by

with P(A and B) beeing the probability of both events occurring simultaneously.

Question 1:

B: Baseball League Championships won, beeing

Y: Championships won by the 10 - 12 years old, beeing

then

P( B and Y)= \frac{ 2 }{ 16 }[/tex]

By definition,

Question 2.A:

Y: Championships won by the 10 - 12 years old, beeing

B: Baseball League Championships won, beeing

then

P( B and Y)= \frac{ 2 }{ 16 }[/tex]

By definition,

Question 2.B:

Z: Championships won by the 13 - 15 years old, beeing

B: Baseball League Championships won, beeing

then

P( Z and B)= \frac{ 1 }{ 16 }[/tex]

By definition,

Question 3.B

Y: Championships won by the 10 - 12 years old, beeing

Z: Championships won by the 13 - 15 years old, beeing

then

B: Baseball League Championships won, beeing

so

By definition,

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