There are five bags each containing identical sets of ten distinct chocolates. One chocolate is picked from each bag.The probability that at least two chocolates are identical is ______

A) 0.3024
B) 0.4235
C) 0.6976
D) 0.8125

Answer: (C) 0.6976

Solution:

To find the probability that no two chocolate are identical = P(Y)

To find the probability that at least two chocolates are identical = P(x):
Formula:

P(x) = 1 – P(Y)

Calculation

No two chocolates identical:

From 1^st bag = Probability = 10/10

From 2^nd bag = Probability = 9/10

From 3^rd bag = Probability = 8/10

From 4^th bag = Probability = 7/10

From 5^th bag = Probability = 6/10

P(Y) = 1(0×9×8×7×6)/(10×10×10×10×10)=0.3024

P(x) = 1 – P(Y) = 1 – 0.3024 = 0.6976