Question

*A bag contains 3 red and 4 blue balls of the same size. Two balls are drawn one after

Answer 1

The first outcome is either red or blue and in the second outcome either blue ball or red ball will be drawn (without replacement) means that the denominator will decrease but in one case blue decreases n red remains . The other case red decreases ( means it is drawn) n blue remains so u will see the fraction above

Answer 2

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