Answer: see below
Step-by-step explanation:
3 Red balls and 4 Blue balls makes a total of 9 balls
1st Draw 2nd Draw Outcome Probability
Red: P(R) = 3/7 Red: P(R₂/R₁) =1/3 Red, Red (3/7) x (1/3) = 1/7
Red: P(R) = 3/7 Blue: P(B₂/R₁) =2/3 Red, Blue (3/7) x (2/3) = 2/7
Blue: P(B) = 4/7 Red: P(R₂/B₁) =1/2 Blue, Red (4/7) x (1/2) = 2/7
Blue: P(B) = 3/7 Blue: P(B₂/B₁) =1/3 Blue, Blue (4/7) x (1/2) = 2/7
Check: Total = 7/7 = 1
Notes:
P(R₂/R₁) means the probability that the 2nd ball is red given that the 1st ball was red. Since you started with 3 red balls out of 7 total balls but previously pulled one red ball out, you now have 2 remaining red balls out of 6 remaining total balls.
2 red / 6 total = 1/3
P(B₂/R₁) means the probability that the 2nd ball is blue given that the 1st ball was red. Since you started with 4 blue balls out of 7 total balls but previously pulled one red ball out, you still have 4 blue balls but only 6 total remaining balls.
4 blue / 6 total = 2/3
P(R₂/B₁) means the probability that the 2nd ball is red given that the 1st ball was blue. Since you started with 3 red balls out of 7 total balls but previously pulled one blue ball out, you still have 3 red balls but only 6 total remaining balls.
3 blue / 6 total = 1/2
P(B₂/B₁) means the probability that the 2nd ball is blue given that the 1st ball was blue. Since you started with 4 red balls out of 7 total balls but previously pulled one blue ball out, now have 3 remaining red balls out of 6 total remaining balls.
3 blue / 6 total = 1/2
See Tree Diagram below
