Answer:
A
Step-by-step explanation:
To solve this you need to use the formulas
P(B|A) = P(A and B)/P(A) and P(A|B) = P(A and B)/P(B)
Let A = all red marbles
Let B = small marbles
Let C = small red marbles
there are 25 total marbles in the bag, then
P(A) = 12/25 (there are 12 red marbles in the bag, big and small)
P(B) = 9/25 (there are 9 small marbles, red and blue)
P(A and B) = 3/25 (there are 3 marbles that are small and red)
To find P(red | small), we use P(A|B) = P(A and B)/P(B) and plug in our known values..
P(red | small) = P( A | B) = (3/25)(9/25)
which simplifies to 3/9, which reduces to 1/3, which equals 0.3333
*Think about it this way too, we know the marble is small, there are 9 small marbles in the bag, 3 are red and 6 are blue, so there is a 3/9 chance of the marble being red if we already know that it's small
To find P(small | red), we use P(B|A) = P(A and B)/P(A) and plug in our known values...
P(small | red) = P(B | A) = (3/25)/(12/25)
which simplifies to 3/12, which reduces to 1/4, which equals 0.25
*Think of it this way too, we know the marble is red, there are 12 red marbles in the bag, 9 are large and 3 are small, so there is a 3/12 chance of the marble being a small red marble if we already know the marble is red
P(red | small) = 0.3333
and
P(small | red) = 0.25
So P(red | small) has the greater probability!
