Answer:
To determine the probabilities and create a tree diagram, we can start by calculating the probability of drawing a specific marble color and then use that to calculate the subsequent probabilities.
Let's go step by step:
Step 1: Calculate the probability of drawing a blue marble (B) or a green marble (G) from the bag.
- P(B) = (number of blue marbles)/(total number of marbles) = 8/13
- P(G) = (number of green marbles)/(total number of marbles) = 5/13
Step 2: Create the tree diagram:
B (8/13)
/ \
B(G) G(B) (5/13)
/ \
B(G) (8/13) G(B) (5/13)
\ /
G(B) (5/13) B(G) (8/13)
Step 3: Calculate the probabilities based on the tree diagram.
4.1 Probability that both marbles drawn are blue:
To calculate the probability that both marbles drawn are blue, we multiply the probabilities along the branch of the tree diagram:
P(Both Blue) = P(B) * P(B) = (8/13) * (8/13) = 64/169
Answer: The probability that both marbles drawn are blue is 64/169.
4.2 Probability that the first marble drawn is blue and the second marble drawn is green:
To calculate the probability that the first marble drawn is blue (B) and the second marble drawn is green (G), we multiply the probabilities along the branch of the tree diagram:
P(First Blue, Second Green) = P(B) * P(G) = (8/13) * (5/13) = 40/169
Answer: The probability that the first marble drawn is blue and the second marble drawn is green is 40/169.
4.3 Probability that the first marble drawn is green or the second marble drawn is green:
To calculate the probability that the first marble drawn is green (G) or the second marble drawn is green (G), we add the probabilities along the branches of the tree diagram:
P(First Green or Second Green) = P(G) + P(G) = (5/13) + (5/13) = 10/13
Answer: The probability that the first marble drawn is green or the second marble drawn is green is 10/13.