Answer:
5/16
Step-by-step explanation:
Step 1: Get rid of miscellanous information and restate the question
A jar contains 3+5+2+6 marbles (16 marbles), 5 of 16 marbles are Green, 6 of 16 marbles are yellow, what are the probabilities of drawing a Green, then a yellow after the green is replaced?
Step 2: find the probability of each draw
5/16 for green and 6/16 for yellow
Step 3: Multiply the odds of each draw
D1 *D2 * D3….etc.
In our case, (5/16)*(6/16) = 30/256
Step 4: simplify
30/256 = 15/128
(I’ll use R,G,B,Y for Red, Green, Blue, Yellow, don’t be surprised)
The probability of picking an item A in a box of N items depends on nA, the amount of items A in the box at the time of picking, with the kinda instinctive value:
p = nA / N
then it means that if you have no green ball, the probability is 0/N = 0, if you only have green balls, it means you have a probability of N/N = 1 = 100%, and if you have as many green balls as non-green balls, you have a probability of nA/(2nA) = 0.5 = 50%.
Here the probability of first picking a green ball (nG=5) in a box of N=3+5+2+6=16 for the 1st pick is:
Probability of choosing a green marble is 5/16
Probability of choosing a yellow marble is 6/16
Both are independent events …so the overall probability is the multiplication of both thats is 30/256=15/128
f ollow me
