In a local auto parts store there are 10 automotive batteries on a shelf. If we

Question

In a local auto parts store there are 10 automotive batteries on a shelf. If we are aware that 4 of the batteries are dead (no charge) but have no idea which of the batteries is dead answer the following:

a.) If we randomly select 3 batteries from the shelf, what is the probability that we have to charge at most one battery before it can be sold?

b.) What is the probability that we select both of the dead batteries if we randomly select 2 batteries from the shelf?

c.) If we select half of the available batteries what is the expected number of dead batteries we would get?

Explanation / Answer

a) Ans: One battery can be charge out og 4 dead batteries in 4C1 ways. Since, one dead battery can be selected in 4C1 ways. Similarly, 2 non-dead batteries can be selected in 6C2 ways.

Hence, the required probability=( 4C1 *6C2)/10C3 = 0.5

b) Ans: Two dead battery can be selected in 4C2 ways. Two batterie are selected from 10 batteries 10C2.

Hence, The probability that we select both of the dead batteries if we randomly select 2 batteries from the shelf =4C2 / 10C2 = 0.133.

c) Ans: If we select half of the batteries, then the number of selected batteries is 5. It can be combination of 2 dead and 3 non-dead batteries. The 2 dead batteries is the half of the total dead batteries (Note, the probability of selecting half of the dead batteries should be approximately near or equal to 0.5). The probability of selecting 2 dead batteries out of 4 is 0.5. Therefore, the expected number of dead batteries is 2.

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