ANSWER :
A. 80/4913
B. 1/68
EXPLANATION :
From the problem, we have a bag that contains 4 Red marbles, 5 Green marbles and 8 lue marbles.
With replacement means that after pulling a marble, it will return to the bag before pulling the second one and so on.
without replacement means that the marble will NOT return to the bag after puling.
The probability formula is possible outcome divided by the total possible outcome.
The total number of marbles is 4 + 5 + 8 = 17, so there are 17 posible outcomes in pulling one marble.
First is we solve for the probability with replacement.
Case 1 : Pulling a red mrble.
Since thre are 4 red marbles, the proibability is 4 red marbles out of 17 marbles.
That's 4/17
Cas 2 : Pulling another red marble for the secondd time.
Since the first marble will be return in the bag, the number of marles is still 17.
Tha 's 4/17
Case 3 : Pulling the third marble as green.
Since there are 5 green marbles, the probability is 5/17
The probability of pulling two red followed by a green marble is the product of these three probbilities.
That will be :
Next is to solve for the probability without replacement.
Case 1 : Pulling the first marble as red.
Since there are 4 red marbles, the probability is 4 red marbles out of 17 marbles.
That's 4/17
Case 2 : Pulling the second marble as red.
Since there is NO replacement, th number of red imarbles in the bag no is 3 and the total number of marbles is 16.
That will be 3/16
Case3 : Pulling the sthird marble as green.
The number of marbles now in the bag after pulling 2 red marbles is 15.
Since there are 5 green marbles, the probability will be 5/15
The probability of pulling two red followed by a green marble is the product of these three probabilities.
