Question

A jar contains 8 red marbles numbered 1 to 8 and 7 blue marbles numbered 1 to 7. A marble is drawn at random from the jar. Find the probability that the marble is blue or even-numbered.

Answer 1

Answer:

Therefore the probability that the marble is blue or even numbered is $\frac{11}{15}$

Step-by-step explanation:

Probability: The ratio of favorable outcomes to the total outcomes.

It is denoted by P.

$Probability= \frac{\textrm{favorable outcomes}}{\textrm{Total outcomes}}$

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)

$=\frac{\textrm{Total number of blue marbles}}{\textrm{Total number of blue marbles}}$

$=\frac{7}{15}$

The probability of getting a even marble  is P(B)

$=\frac{\textrm{The number of even number marbles}}{\textrm{Total number of marbles}}$

$=\frac{7}{15}$

The probability of getting a even numbered blue marble P(A∩B)

$=\frac{3}{16}$

P(blue marble or even- numbered)

=P(A∪B)

=P(A)+P(B)-P(A∩B)

$=\frac{7}{15} +\frac{7}{15}-\frac{3}{15}$

$=\frac{11}{15}$

Therefore the probability that the marble is blue or even numbered is $\frac{11}{15}$