Question

URGENT

A box contains 18 large marbles and 16 small marbles. Each marble is either green or white. 7 of the large marbles are green, and 7 of the small marbles are white. If a marble is randomly selected from the box, what is the probability that it is large or green? Express your answer as a fraction or a decimal number rounded to four decimal places.

Answer 1

p(large or green) = 0.794

Explanation:

• A box contains 18 large marbles and 16 small marbles

• Each marble is either green or white

• 7 of the large marbles are green, and 7 of the small marbles are white

If a marble is randomly selected from the box, we need to find the

probability that it is small or green

1. Find P(large) ⇒ P(l)

2.Find P(green) ⇒ P(g)

3. Find P(large and green) ⇒ P(l and g)

4. Use the rule P(large or green) = P(l) + P(g) - P(l and g)

∵ The box contains 18 large marbles and 16 small marbles

∴ The total number of marbles = 18 + 16 = 34

∴ P(l) = 18/34

∵ There are 7 large green marbles

∵ There are 18 large marbles

∴ P(l and g) = 7/34

• 7 large green marbles
• 9 small green marbles
• number of green marbles = 7+9 = 16

∴ P(g) = 16/34

∵ P(large or green) = P(l) + P(g) - P(l and g)

∴ P(large or green) = 18/34 + 16/34 - 7/34

∴ P(large or green) = 27/34

= 0.7941176471

If a marble is randomly selected from the box, then the probability that it is large or green is 0.794