How do I find the probability of P(G OR E) ? please help explain.

Question

Suppose that you have 7 cards. 3 are green and 4 are yellow. The 3 green cards are numbered 1, 2, and 3. The 4 yellow cards are numbered 1, 2, 3, and 4. The cards are well shuffled. You randomly draw one card.

• G = card drawn is green

• Y = card drawn is yellow

• E = card drawn is even-numbered

1. List the sample space. (Type your answer using letter/number combinations separated by commas. Example: G1, Y1, ...)

G1, G2, G3, Y1, Y2, Y3, Y4

1. Enter the probability as a fraction.

P(G) =  3/7

1. Enter the probability as a fraction.

P(G | E) =  1/3

1. Enter the probability as a fraction.

P(G AND E) =  1/7

1. Enter the probability as a fraction.
2. P(G OR E) = ?

Answer 1

P(G or E) = probability of picking a green card or picking an even-numbered card.

Formula:

P(G) + P(E) - P(G and E) = 3/7 + 3/7 - 1/7 = 5/7

explanation: you want to add the probability of getting a green card and even-numbered card, but you don't want to count the intersecting card twice (G2). Thats why we minus P(G and E) from the sum of P(G) and P(E).