Question

Consider rolling two four sided dice. One die is blue and the other is green.

(a) State the sample space.

(b) Compute the probability of getting two even numbers.

(c) Compute the probability of getting an even sum if the blue die rolls a 2.

What is the probability of drawing a four or a heart when drawing a single card from a standard deck of cards.

Answer 1

(a)
Sample Space = {(Blue = 1, Green = 1), (Blue = 1, Green = 2), (Blue = 1, Green = 3), (Blue = 1, Green = 4), (Blue = 2, Green = 1), (Blue = 2, Green = 2), (Blue = 2, Green = 3), (Blue = 2, Geen = 4), (Blue = 3, Green = 1, (Blue = 3, Green = 2), (Blue = 3, Green = 3), (Blue = 3, Green = 4), (Blue = 4, Green = 1), (Blue = 4, Green = 2), (Blue = 4, Green = 3), (Blue = 4, Green = 4)}

(b)

Total number of events = 16

Favorable Events = {(Blue = 2, Green = 2), (Blue = 2, Green = 4), (Blue = 4, Green = 2)< (Blue = 4, Green = 4)} : 4 Nos.

So,

P(two even numbers) = 4/16 = 0.25

(c) Sum = Even. Blue = 2.

Favorable Events = {Blue = 2, Green = 2), (Blue = 2, Green = 4)}: 2 Nos.

So,

P(Sum = Even & Blue = 2) = 2/16 = 0.125

(d) Total number of cards = 52

Number of Four = 4

Number of Heart = 13

Number of Four & Heart = 1

By Addition Theorem:
P(Four OR Heart) = P(Four) + P(Heart) - P(Four & Heart)

                           = 4/52 + 13/52   - 1/52

                             = 0.0769 + 0.25 - 0.0192

                              = 0.3077