How many times must a man toss a fair coin so that the probability of having at least one head is more than 90%?
Let us assume that, man tosses the coin n times. Thus, n tosses are the Bernoulli trials
∴ Probability of getting head at the toss of the coin
Let us assume,
It is given in the question that,
Probability of getting at least one head >
1 – P (x = 0) > 0.9
Hence, the minimum value of n satisfying the given inequality = 4
∴ The man have to toss the coin 4 or more times
An urn contains 25 balls of which 10 balls bear a mark 'X' and the remaining 15 bear a mark 'Y'. A ball is drawn at random from the urn, its mark is noted down and it is replaced. If 6 balls are drawn in this way, find the probability that:
(i) All will bear 'X' mark.
(ii) Not more than 2 will bear 'Y' mark.
(iii) At least one ball will bear 'Y' mark.
(iv) The number of balls with 'X' mark and 'Y' mark will be equal.
One of the boxes has been selected at random and a single marble is drawn from it. If the marble is red, what is the probability that it was drawn from box A?, box B?, box C?
Assume that the chances of a patient having a heart attack are 40%. It is also assumed that a meditation and yoga course reduce the risk of heart attack by 30% and prescription of certain drug reduces its chances by 25%. At a time a patient can choose any one of the two options with equal probabilities. It is given that after going through one of the two options the patient selected at random suffers a heart attack. Find the probability that the patient followed a course of meditation and yoga?
An electronic assembly consists of two subsystems, say, A and B. From previous testing procedures, the following probabilities are assumed to be known:
P (A fails) = 0.2
P (B fails alone) = 0.15
P (A and B fail) = 0.15
Evaluate the following probabilities:
(i) P (A fails | B has failed)
(ii) P (A fails alone)
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.
Choose the correct answer in each of the following: