Respuesta :
Answer:
[tex]0.7308[/tex]
Step-by-step explanation:
Given: A box contains 15 large marbles and 11 small marbles. Each marble is either green or white. 8 of the large marbles are green, and 5 of the small marbles are white.
To find: probability that a marble randomly selected is small or green
Solution:
Total number of marbles = [tex]15+11=26[/tex]
Number of small marbles that are white = 5
Also, each marble is either green or white.
So,
Number of small marbles that are green = [tex]11-5=6[/tex]
Total number of green marbles = Number of large marbles that are green + Number of small marbles that are green
= [tex]8+6=14[/tex]
Probability = Number of favorable outcomes ÷ Total number of outcomes
Let E denotes the event that a marble selected is small.
Let F denotes the event that a marble selected is green.
P(E) = Number of small marbles ÷ Total number of marbles
= [tex]\frac{11}{26}[/tex]
P(F) = Number of green marbles ÷ Total number of marbles
= [tex]\frac{14}{26}[/tex]
P(E∩F) = [tex]\frac{6}{26}[/tex]
Probability that it is small or green = P(E∪F)
= P(E) + P(F) -P(E∩F)
= [tex]\frac{11}{26}+\frac{14}{26}-\frac{6}{26}[/tex]
[tex]=\frac{11+14-6}{26} \\\\ =\frac{19}{26} \\\\=0.7308[/tex]
