SOLUTION: You choose a tile at random from a bag containing 2 A's, 3 B's, and 4 C's. You replace the first tile in the bag and then choose again. Find the probability. P(A and A)

Algebra ->  Probability-and-statistics -> SOLUTION: You choose a tile at random from a bag containing 2 A's, 3 B's, and 4 C's. You replace the first tile in the bag and then choose again. Find the probability. P(A and A)       Log On


   



Question 1188653: You choose a tile at random from a bag containing 2 A's, 3 B's, and 4 C's. You replace the first tile in the bag and then choose again. Find the probability.

P(A and A)
P(A and B)
P(C and C)
P(B and C)
P(B and B)

Answer by ikleyn(52787) About Me  (Show Source):
You can put this solution on YOUR website!
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The total number of tiles is   A + B + C = 2 + 3 + 4 = 9.


When you draw first tile and then replace it, you return everything to the original state.   THEREFORE


P(A and A) = %282%2F9%29%2A%282%2F9%29 = 4%2F81.


P(A and B) = %282%2F9%29%2A%283%2F9%29 = 2%2F27.


P(C and C) = %284%2F9%29%2A%284%2F9%29 = 16%2F81.


P(B and C) = %283%2F9%29%2A%284%2F9%29 = 4%2F27.


P(B and B) = %283%2F9%29%2A%283%2F9%29 = 1%2F9%29.

Solved.