The probability that the second marble drawn is yellow is 103/ 245.
Let's break this down step by step.
First, we'll find the probability of drawing a white marble from bag A:
Probability of drawing a white marble from bag A = Number of white marbles in bag A / Total number of marbles in bag A
Probability = 3/ 3+4 = 3/7
Next, the probability of drawing a yellow marble from bag B given that a white marble was drawn from bag A:
Probability of drawing a yellow marble from bag B = Number of yellow marbles in bag B / Total number of marbles in bag B
Probability = 6/6+4 = 6/10 = 3/5
Now, let's calculate the probability of drawing a black marble from bag A:
Probability of drawing a black marble from bag A = Number of black marbles in bag A / Total number of marbles in bag A
Probability = 4/ 3+4 = 4/7
Lastly, the probability of drawing a yellow marble from bag C given that a black marble was drawn from bag A:
Probability of drawing a yellow marble from bag C = Number of yellow marbles in bag C / Total number of marbles in bag C
Probability= 2/ 2+5 = 2/ 7
Now, let's find the overall probability of drawing a yellow marble as the second marble:
This probability will be the sum of the probabilities of drawing a white marble from bag A and then a yellow marble from bag B, plus the probabilities of drawing a black marble from bag A and then a yellow marble from bag C.
Probability = Probability of drawing white marble from bag A * Probability of drawing yellow marble from bag B + Probability of drawing black marble from bag A * Probability of drawing yellow marble from bag C
Probability = ( 3/ 7 )×( 3/5 )+( 4/7 )×( 2/7 )
Let's compute this:
( 3/ 7 )×( 3/5 )+( 4/7 )×( 2/7 )= 9/ 35 + 8/ 49
= 63+40/ 245
= 103/ 245
Therefore, the probability that the second marble drawn is yellow is 103/ 245.
Question
bag a has $3$ white marbles and $4$ black marbles. bag b has $6$ yellow marbles and $4$ blue marbles. bag c has $2$ yellow marbles and $5$ blue marbles. a marble is drawn at random from bag a. if it is white, a marble is drawn at random from bag b, otherwise, if it is black, a marble is drawn at random from bag c. what is the probability that the second marble drawn is yellow?