Probability Tes...

It is known that \(10 \%\) of certain articles manufactured are defective. What is the probability that in a random sample of 12 such articles, 9 are defective?

A factory has two machines \(A\) and \(B\). Past record shows that machine A produced \(60 \%\) of the items of output and machine B produced \(40 \%\) of the items. Further, \(2 \%\) of the items produced by machine A and \(1 \%\) produced by machine B were defective. All the items are put into one stockpile and then one item is chosen at random from this and is found to be defective. What is the probability that it was produced by machine B?

A card from a pack of 52 cards is lost. From the remaining cards of the pack, two cards are drawn and are found to be both diamonds. Find the probability of the lost card being a diamond.

If \(A\) and \(B\) are two events such that \(P ( A \cup B )\)= \(\frac{5}{6}\) , \(P ( A \cap B )\) = \(\frac{1} {3}\), \(P ( B )\) = \(\frac{1}2\), then the events \(A\) and \(B\) are:

Find the probability of getting 5 exactly twice in 7 throws of a die.

There are \(5 \%\) defective items in a large bulk of items. What is the probability that a sample of 10 items will include not more than one defective item?

A dice is thrown again and again until three sixes are obtained. Find the probability of obtaining the third six in the sixth throw of the die.

Find the probability of throwing at most 2 sixes in 6 throws of a single dice.

A fair coin is tossed independently four times. The probability of the event "the number of times heads show up is more than the number of times tails show up" is:

In a game, a man wins a rupee for a six and loses a rupee for any other number when a fair die is thrown. The man decided to throw a die thrice but to quit as and when he gets a six. Find the expected value of the amount he wins/loses.