Math homework school

Question

Suppose a jar contains 20 red marbles and 32 blue marbles. If you reach in the jar and pull out 2 marbles at random at the same time, find the probability that both are red.

Answer 1

Red marbles: 20

Blue marbles: 32

Total number of red and blue marbles is 52

Pairs of two in 52:

52/2 = 26 (one can withdraw two marbles - without replacement - 26 times).

Pairs of two in 20:

20/2 = 10 (one can withdraw two red marbles - without replacement - 10 times)

26 - total number of cases to withdraw two marbles (of any combination of colors)

10 - number of desired cases (to withdraw two reds)

10/26 = 5/13 ≅ 0.38 → probability to withdraw two reds at once (without replacement)

Answer 2

P(1st red) = 20/32= 5/8

P(2nd red)= 19/31

P(1st two red) = 5/8 times 19/31 = about 38% chance