Working with 3rds

Question

There are 4 red marbles and 8 green marbles in a box. If Emma randomly select a marble from the box, what is the probability of her selecting a red marble?

Answer 1

Answer: 1 / 3

Explanation: The key formula is P(E) = size of E / size of S, where E, an event, is a subset of the sample space S. See below for more.

The sample space for Emma's selection is the set of possible outcomes S, which we may write as follows:

S = {R₁, R₂, R₃, R₄, G₁, G₂, G₃, G₄, G₅, G₆, G₇, G₈}.

The event E_R = "Emma selecting a red marble." is represented by the four outcomes in the sample space labeled R, while the event E_G = "Emma selecting a green marble." is represented by the eight outcomes in the sample space labeled G. We could write these as subsets of S also:

E_R = {R₁, R₂, R₃, R₄} and E_G = {G₁, G₂, G₃, G₄, G₅, G₆, G₇, G₈}

Since there are four outcomes where Emma selects a red marble, and 4 + 8 = 12 events total, the probability that Emma selects a red marble is 4 / 12 which simplifies to 1 / 3, after cancelling the common factor 4. We might write this as in the key formula:

P(E_R) = size of E_R / size of S = 4 / 12 = 1 / 3.

Hope this helps.