Exactly one side of a certain 10-sided die are red. What is the probability that Kumar rolls the die 3 times and the die lands with a red side up for the first time on the third roll? Options
A) 0.09
B) 0.1
C) 0.081
D) 0.091
E) 0.074
Total no. of sides = 10   Side that are red = 1   Probability that the die lands with red side up = 1/10   Therefore, Probability that the die does not land with red side up = 1 - 1/10 = 9/10   Probability that Kumar rolls the die 3 times and the die lands with a red side up for the first time on the third roll   = (1st roll - non red face) X (2nd roll - non red face) X (3rd roll - red face)   = (9/10) X (9/10) X (1/10)   = 81/1000= 
<gadget id="calculator">81/1000</gadget>
<output>81/1_000 = around 0.081</output>
0.081   0.081
<result>C</result>
Exactly one side of a certain 10-sided die are red. What is the probability that Kumar rolls the die 3 times and the die lands with a red side up for the first time on the third roll?