Respuesta :
Answer:
Therefore the probability that the marble is blue or even numbered is [tex]\frac{11}{15}[/tex]
Step-by-step explanation:
Probability: The ratio of favorable outcomes to the total outcomes.
It is denoted by P.
[tex]Probability= \frac{\textrm{favorable outcomes}}{\textrm{Total outcomes}}[/tex]
Given that a jar contains 8 red marbles and 7 blue marbles.
Total number of marbles = (8+7) = 15
Let A = Event of getting a blue marble
B= Event of getting of even marble.
Even number blue marbles are 2, 4,6
Even number red marbles are 2, 4,6,8
The number of even marbles are =(3+4)=7
The probability of getting a blue marble is P(A)
[tex]=\frac{\textrm{Total number of blue marbles}}{\textrm{Total number of blue marbles}}[/tex]
[tex]=\frac{7}{15}[/tex]
The probability of getting a even marble is P(B)
[tex]=\frac{\textrm{The number of even number marbles}}{\textrm{Total number of marbles}}[/tex]
[tex]=\frac{7}{15}[/tex]
The probability of getting a even numbered blue marble P(A∩B)
[tex]=\frac{3}{16}[/tex]
P(blue marble or even- numbered)
=P(A∪B)
=P(A)+P(B)-P(A∩B)
[tex]=\frac{7}{15} +\frac{7}{15}-\frac{3}{15}[/tex]
[tex]=\frac{11}{15}[/tex]
Therefore the probability that the marble is blue or even numbered is [tex]\frac{11}{15}[/tex]
