Question

You have a bag with 24 blue marbles (B) and 16 red marbles (R). You are going to pick 3, without replacing the first or the second marble.

a. Create a complete tree diagram for the outcomes of picking the 3 marbles

b. What is the probability that the first is Red

c. What is the probability that the second is Blue

d. What is the probability that you will get at least one Blue

Answer 1

		Blue	Red	Total
		24	16	40
1st Marble						3rd Marble
	Probability of Blue , P(B) = 24/40 = 0.6						When the 1st Marble is blue
	Probability of Red , P(R) = 16/40 = 0.4						When the 2nd Marble is blue
							Probability of Blue , P(B) = 22/38 = 0.579
							Probability of Red , P(R) = 16/38 = 0.421
2nd Marble
	When the 1st Marble is blue
	Probability of Blue , P(B) = 23/39 = 0.590						When the 1st Marble is blue
	Probability of Red , P(R) = 16/39 = 0.410						When the 2nd Marble is Red
							Probability of Blue , P(B) = 23/38 = 0.605
	When the 1st Marble is Red						Probability of Red , P(R) = 15/38 = 0.395
	Probability of Blue , P(B) = 24/39 = 0.615
	Probability of Red , P(R) = 15/39 = 0.385						When the 1st Marble is Red
							When the 2nd Marble is blue
							Probability of Blue , P(B) = 23/38 = 0.605
							Probability of Red , P(R) = 15/38 = 0.395
							When the 1st Marble is Red
							When the 2nd Marble is Red
							Probability of Blue , P(B) = 24/38 = 0.632
							Probability of Red , P(R) = 14/38 = 0.368

0.579 Blu 0.59 Blue 0.421. Red リ Blue Blue 0.605 0.41 0.6 Red 0.39 Red Blue 0.605 0.4 Blue 0.615 0.395 Red Red Blue 0.632 Red 0.385 Red 0.5

B. The probability that the first marble is red = 0.4.

C. The probability that the second marble is blue

= P

= 0.6*0.59 + 0.4 * 0.615 = 0.6

D. Probability that u will get at least one blue = 1- Probability of getting no blues( or all reds)

Probability of getting all reds = 0.4 * 0.385 * 0.568 = 0.08747

Therefore, Probability that u will get at least one blue = 1 - 0.08747 = 0.91253 = 91.253%.

Hope I answered your query.