Explanation:
there are
1 red marble
3 blue marbles
4 green marbles
in the box.
that means there are 8 marbles in the box. which gives us 8 different outcomes for pulling randomly 1 marbles.
the probability for each of these 8 outcomes is equal : 1/8.
remember, the probability is always the number of desired cases over the number of total possible cases.
so, the probability of pulling a red marble is :
1 desired case
8 total cases
->
1/8 or 0.125
the probability of pulling a blue marble is :
3 desired cases
8 total cases
->
3/8 or 0.375
the probability of pulling a green marble is :
4 desired cases
8 total cases
->
4/8 = 1/2 or 0.5
now the experiment is pulling 2 marbles in a row, but the first pulled marble is put back into the box again.
this makes this a combined event, where the first AND the second event must fulfill the desired over total cases.
if the 2 events are independent (not overlapping or influencing each other), then we can simply multiply the probabilities. which is the case here, because the first marble is put back.
why ?
because now we have 8 possible outcomes for the first ball, and again 8 possible outcomes for the second ball, and when we combine all possibilities from the first with all possibilities from the second pull, we get 8×8 = 64 possible outcomes :
red. red
red. blue1
red. blue2
red. blue3
red. green1
...
green4 green4
so, the probability to pull a blue ball first is
3/8
and the probability to pull a blue ball second is
3/8 too
the combined probability of the combined event is
3/8 × 3/8 = 9/64
we have 3×3 = 9 desired outcomes of combining 3 blue and 3 blue balls out of the total of 64 possible outcomes.