8/15
Explanation:
Step 1:
Total number of pins for the first draw = 10
Number of blue pins = 3
Number of green pins = 7
Probability of the first pin drawn is blue is 3/10
For the second draw, without replacement
Total sample space = 9
Number of blue pins = 2
Probability that the second pin drawn is also blue is 2/9 [because the pin is drawn without replacement]
So probability that both the pins drawn are blue is 3/10*2/9 = 6/90
Step 2 :
To find the Probability that both the pins drawn are green
Total sample space for the first draw = 10
Number of green pins = 7
Probability of the first pin drawn is green is 7/10
For the second draw, without replacement
Total sample space = 9
Number of green pins = 6
Probability that the second pin drawn is also green is 6/9 [because the pin is drawn without replacement]
So probability that both the pins drawn are green is 7/10*6/9 = 42/90
Step 3:
Probability that both the pins drawn are of the same color, that is both are blue or both or green is
6/90 + 42/90 = 48/90 = 8/15