What’s the probability of a marble being red, not yellow, either red or green & neither red nor green?

Question

A marble is selected at random from a jar containing 5 red marbles, 2 yellow marbles & 3 green marbles. What is the probability that a)the marble is red

b)the marble is not yellow

c)the marble is either red or green

d)the marble is neither red nor green

Answer 1

R = red marble

Y = yellow marble

G = green marble

There are 10 marbles in a jar (5 reds, 2 yellows, and 3 greens).

P(R) = 5/10 = 1/2 = 0.5

P(Y^c) = 1 - P(Y) = 1 - (2/10) = 8/10 = 4/5 = 0.8

P(R ∪ G) = P(R) + P(G) - P(R ∩ G) = (5/10) + (3/10) - 0 = 8/10 = 0.8

P[(R ∪ G)^c] = P(Y) = 2/10 = 1/5 = 0.2

The probability that the marble is red is 0.5.

The probability that the marble is not yellow is 0.8.

The probability that the marble is either red or green is 0.8.

The probability that the marble is neither red nor green is 0.2.

Answer 2

A marble is selected at random from a jar containing 5 red marbles, 2 yellow marbles & 3 green marbles. What is the probability that

a)the marble is red

There are 10 total marbles and 5 red, so probability marble is red is 5/10 = 1/2

b)the marble is not yellow

8 marbles are not yellow, so probability marble is not yellow is 8/10 = 4/5

c)the marble is either red or green

8 marbles are either red or green, so probability is 8/10 = 4/5

d)the marble is neither red nor green

2 marbles are neither red or green, so probability is 2/10 = 1/5