GATE (GA) Textile 2021 Question Paper Solution | GATE/2021/GA/08

Q.8	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

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Given-

There are total 5 bags.

Probability of picking one chocolate from 1st bag= $\frac{10}{10}$

Probability of picking one chocolate from 2nd bag= $\frac{9}{10}$

Probability of picking one chocolate from 3rd bag= $\frac{8}{10}$

Probability of picking one chocolate from 4th bag= $\frac{7}{10}$

Probability of picking one chocolate from 5th bag= $\frac{6}{10}$

The probability that at least two chocolates are non identical= $\frac{10\times9\times8\times7\times6}{10\times10\times10\times10\times10 }$

The probability that at least two chocolates are non identical= $0.3024$

The probability that at least two chocolates are identical=1-0.3024

The probability that at least two chocolates are identical=0.6976