Question

The table shows the number of championships won by the baseball and softball leagues of three youth baseball divisions organized by age groups. 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. A= p(y|b)= A0 B= p(z|b)= A1 C= p(y or z |b)= A2

Answer 1

Answer:

0.5 or 50%

Step-by-step explanation:

• Total number of championships won = 3+2+1+7+2+1=16
• Total Number of winners in baseball league, n(B)= 3+2+1=6
• Number of Wins in the Ages 10 - 12 division, n(Y) =2
• Number of Wins in the Ages 13-15 division, n(Z) =1

The probability that the winning team is in the Ages 10 - 12 division given that it is in the baseball league:

$P(Y|B)=\dfrac{P(Y \cap B)}{P(B)} \\=\dfrac{2/16}{6/16}\\=\dfrac{2}{6}$

The probability that the winning team is in the Ages 13 - 15 division given that it is in the baseball league:

$P(Z|B)=\dfrac{P(Z \cap B)}{P(B)} \\=\dfrac{1/16}{6/16}\\=\dfrac{1}{6}$

Therefore:

$P(Y or Z|B)=\dfrac{2}{6}+\dfrac{1}{6}\\=\dfrac{3}{6}\\\\=0.5$