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Answer:
A junk box in your room contains fourteen old batteries, seven of which are totally dead.
So, number of good batteries =
a) The first two you choose are both good.
There is a 7/14 chance that we will pick a good battery.
Now there are 13 batteries left and out of that there are only 6 good ones remaining, so this becomes 6/13.
So, combined probability is =
= 0.23
b) At least one of the first three works.
And at least one is good battery, we get :
c) The first four you pick all work.
There is a probability of 7/14 for the first one to work, 6/13 for the second, 5/12 for the third and 4/11 when the fourth is good, combined we get by multiplying all:
d) You have to pick five batteries to find one that works.
This condition means that we pick 4 bad batteries and 1 good battery.
The probability of picking 4 bad batteries is -
Since there are 7 good batteries remaining in 10 batteries so we will multiply 7/10 in 0.0344 to know the fifth one that finally works.
This becomes =