Question

A box contains 14 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 white? Express your answer as a fraction or a decimal number rounded to four decimal places.

Answer 1

Answer:

Step-by-step explanation:

Given that:

Number of Large Marbles = 14

Number of Small Marbles = 11

Number of Green large marbles = 8

Number of White small marbles = 5

We can now find the number of white large marbles and green small marbles from the information stated above.

No of white large marble = total large marble minus green large marble

= 14-8

= 6

No of green small marbles = Total small marbles minus white small marble.

= 11-5

= 6

Let the following be represented

( X,Y, Z,Q ) as follows:

Let Y be the event of drawing small marble

Let X be the event of drawing large marble

Let Q be the event of drawing white marble

Let Z be the event of drawing green marble.

Since, only one marble is drawn at a time we calculate,

P( X ) = 14/25

P( Y) = 11/25

P(Z) = 14/25

P( Q) = 11/25

P(Y∪Q)=P(Y)+P(Z)−P(Y∩Z)...(1)

We need to find the value of

P(Y∩Z)

In 11 small marbles there are 6 green marbles so the value of P(Y∩Z) is given by P(Y∩Z)=6/11

Therefore, substitute the values in equation 1.

P(Y∪Z)=P(Y)+P(Z)−P(Y∩Z)=11/25+14/25-

6/11

=0.44+0.56−0.5455

= 1-0.5455

= 909/2000

= 0.4545

Then, one can conclude that the probability of drawing a small or green marble is 0.4545