Probability Tes...

Consider the experiment of throwing a die, if a multiple of 3 comes up, throw the die again and if any other number comes, toss a coin. Find the conditional probability of the event 'the coin shows a tail', given that at least one die shows as \(3\).

How many times must a man toss a fair coin so that the probability of having at least one head is more than \(90 \%\)?

Two cards are drawn at random and without replacement from a pack of \(52\) playing cards. Find the probability that both the cards are black:

Ten eggs are drawn successively, with replacement, from a lot containing \(10 \%\) defective eggs. Find the probability that there is at least one defective egg.

A pair of dice is thrown. Find the probability of obtaining a sum of 8 or getting an even number on both the dice.

A bag contains 4 red and 4 black balls, another bag contains 2 red and 6 black balls. One of the two bags is selected at random and a ball is drawn from the bag which is found to be red. Find the probability that the ball is drawn from the first bag.

A dice is tossed thrice. Find the probability of getting an odd number at least once:

If a leap year is selected at random, what is the chance that it will contain 53 Tuesdays?

An experiment succeeds twice as often as it fails. Find the probability that in the next six trials, there will be at least 4 successes.

Bag I contains 3 red and 4 black balls and Bag II contains 4 red and 5 black balls. One ball is transferred from Bag I to Bag II and then a ball is drawn from Bag II. The ball so drawn is found to be red in colour. Find the probability that the transferred ball is black.