1) In a batch of 10 articles, 4 articles are defective. 6 articles are taken from the batch for inspection.
If more than 2 articles in this batch are defective, the whole batch is rejected.
Find the probability that the batch will be rejected.
2)An author writes a good book with a probability of 1/2 .
If it is good it is published with a probability of 2/3.
If it is not, it is published with a probability of 1/4.
Find the probability that he will get atleast one book published if he writes two.
391) i am not sure but no other idea strking me as of now.. X be no :of defective articles picked. so we need to find P[X=3]+P[X=4]+P[X=5]+P[X=6] = 3/10C6 +4/10C6+5/10C6+6/10C6 =18/10C6
4Sorry .....
ANSWER for 1st one is 19/42
I think the mistake may be in considering 5 or 6 defective articles since only max 4 r possible
4Hey I got the solution now
P = 6C3 4C3 + 6C2 4C3
6C6 4C0 + 6C5 4C1 + 6C4 4C2 +6C34C3 + 6C2 4C4
= 19 / 42 ANSWER
4Second ans copied from a link given by b555
A random book will be published with probability 1/2 x 2/3 + 1/2 x 1/4 = 11/24
. The probability of him writing two books none of which gets published must therefore be
[1 - (11/24)]2
The probability that he we will get at least one published is therefore:
1 - (1 - 11/24) 2 = 407/576 ANSWER
4More on PROBABILITY
3 ) Two cards are drawn from a well shuffled pack of 52 cards. Find the probability that one of them is a red card & the other is a queen.
4)Each of the 'n' passengers sitting in a bus may get down from it at next stop with probability
P.Moreover, at the next stop either no passenger or exactly one passenger boards the bus. The
probability of no passenger boarding the bus at the next stop being Po . Find the probability that when
the bus continues on its way after the stop, there will again be 'n' passengers in the bus.