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,

the correct functions are

h(x) = 3x + 2  

g(x) = 2^x

step-by-step explanation:

i proceed to calculate the different values ​​of k (x)

case 1)  k(x) = g(x) ∘ h(x)

g(x) ∘ h(x)=g(h(x))

k(x) = [2]^[3x + > is the option  4. k(x) = 2^(3x + 2 )

case 2)  k(x) = g(x) + h(x)

k(x) = [2^x]+[3x + 2]=2^x+3x+> is the option  1.) k(x) = 2^x + 3x + 2

case 3)k(x) = h(x) ÷ g(x)

k(x) =  [3x + 2]/[2^x]=3x/(2^x)+2/(2^x)=3x*(2^-x)+2^(1-x)

is the option  3.)   k(x) = (3x)2^(-x) + 2^(-x + 1 )

case 4)k(x) = g(x) - h(x)

k(x) =  [2^x]-[3x + 2]=2^x-3x-> is the option  2.) k(x) = 2^x - 3x - 2 

case 5)  k(x) = g(x) × h(x)

k(x) = [2^x]*[3x + > is the option  5.) k(x) = 2^x(3x + 2)

case 6)k(x) = h(x) ∘ g(x)

h(x) ∘ g(x)=h(g(x))

k(x)=3*[2^x]+> is the option  6. k(x) = 3(2^x) +2