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 green?

Answer 1

Answer is 0.7536

Explanation:

Large Marbles = 14 Small Marbles = 11

Green LM = 8 Green SM = 6

White LM = 6 White SM = 5

QUESTION:

If a marble is randomly selected from the box, what is the probability that it is small or it is green?

Note the use of "or" and not "and".

SOLUTION:

In this case, the two events - small marble & green marble - are NOT mutually exclusive. This means that sometimes they occur together. We can have a marble that is both small and green!

The formula for this probability is hence

P(A or B) = P(A) + P(B) - P(A and B)

Let A = The event that the selected marble is small

B = The event that the selected marble is green

Total number of marbles = 14 + 11 = 25

P(A or B) = 11/25 + (8+6)/25 - [P(A) × P(B)]

P(A or B) = 11/25 + 14/25 - [11/25 × 14/25]

= 0.44 + 0.56 - 0.2464 = 1 - 0.2464 = 0.7536

Answer 2

Answer: 19/25.

Explanation:

Given data:

Large marbles = 14

Small marbles = 11.

8 large marbles = green.

5 of small marbles = white.

Solution:

If 8 of large marbles are green, therefore the remaining 6 are white.

Likewise for the small marbles the remaining 6 are green marbles.

Total number of marbles = 14 + 11

= 25.

P(small or green) = P(small) + P (green) – P (Both)

= 11/25 + 14/25 – 6/11

= 19/25