There is a bag filled with 2 blue, 4 red and 5 green marbles. A marble is taken at random from the bag, the colour is noted and then it is replaced.
Another marble is taken at random.
What is the probability of getting 2 the same colour?

Work Shown:

2 blue, 4 red, 5 green

2+4+5 = 11 total

P(blue) = probability of getting one blue marble

P(blue) = (number of blue)/(number total)

P(blue) = 2/11

A = P(2 blue) = (2/11)*(2/11) = 4/121

P(red) = 4/11

B = P(2 red) = (4/11)*(4/11) = 16/121

P(green) = 5/11

C = P(2 green) = (5/11)*(5/11) = 25/121

Add the values of A,B, and C to get the probability of getting two of the same color

A+B+C = 4/121+16/121+25/121 = 45/121

This is approximately equal to 0.3719 which is roughly a 37.19% chance of happening

Side note: we can add A,B, and C because they are mutually exclusive events.

answer: all of the odd numbers were opened

the first person was the one that was opening all of the lockers. since one is odd, this causes all of the odd number lockers to be opened in the end.