Question

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. If a marble is randomly selected from the box, what is the probability that it is small or green? Express your answer as a fraction or a decimal number rounded to four decimal places.

Answer 1

`0.7308`

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 =
`15+11=26`

Number of small marbles that are white = 5

Also, each marble is either green or white.

So,

Number of small marbles that are green =
`11-5=6`

Total number of green marbles = Number of large marbles that are green + Number of small marbles that are green

=
`8+6=14`

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

=
`(11)/(26)`

P(F) = Number of green marbles ÷ Total number of marbles

=
`(14)/(26)`

P(E∩F) =
`(6)/(26)`

Probability that it is small or green = P(E∪F)

= P(E) + P(F) -P(E∩F)

=
`(11)/(26)+(14)/(26)-(6)/(26)`

`=(11+14-6)/(26) \\\\ =(19)/(26) \\\\=0.7308`