probability question

Question

what is rhe proboikoty of drawing two blue marbles if the first marble is placed back in the baag before the second draw

Answer 1

Another way to look at it using Sofia's last example with 4 blue & 10 total.

1st draw (P)B = 4/10 or 2/5

2nd draw (P)B = 4/10 or 2/5 (same probability because the 1st marble is replaced)

Probability of 2 blues in 2 draws is then 2/5 x 2/5 = 4/25, or 16%.

Answer 2

If you have M marbles in the bag and B of them are blue, then the probability of drawing one blue marble from the bag is B / M

If you return the first marble to the bag before drawing the second marble, the probability of the second marble being blue is also B / M

Thus the probability of both marbles being blue is B² / M²

For example, if you have a bag with 4 blue marbles, 3 red marbles, 2 green marbles, and 1 yellow marble (total of 10 marbles), then the probability to draw two blue marbles is 4²/10² = 16/100 =16%