Q. 263.7( 3 Votes )
A man wins a rupee for head and loses a rupee for tail when the coin is tossed. Suppose that he tosses once and quits if he wins but tries once more if he loses on the first toss. Find the probability distribution of the number of rupees the man wins.
Let X be the number of rupees the man won/lost.
Let n be the number of throws required to get a head.
We have two cases, that is
(i). The man tosses once, head comes up, and he quits. (head means he won)
(ii). The man tosses once; tail comes up then he tosses again, tail comes up. (tail means he lost)
(ii). The man tosses, tail comes up then he tosses again, head comes up. (tail means he lost & head means he won)
In Case (i),
The man tosses once, head comes up, and he quits.
Here, number of throws (n) = 1
Amount won/lost (X) = 1
In Case (ii),
The man tosses once; tail comes up then he tosses again, tail comes up.
Here, number of throws (n) = 2
Amount won/lost (X) = -2
In Case (iii),
The man tosses once, tail comes up then he tosses again, head comes up.
Here, number of throws (n) = 2
Amount won/lost (X) = 0
We have the table:
Thus, the probability distribution is
Hence, the answer is obtained.
Rate this question :
A box has 100 pens of which 10 are defective. What is the probability that out of a sample of 5 pens drawn one by one with replacement at most one is defective?Mathematics - Exemplar
State True or False for the statements in the Exercise.
If A, B and C are three independent events such that P(A) = P(B) = P(C) = p, then
P (At least two of A, B, C occur) = 3p2 – 2p3Mathematics - Exemplar
A random variable X has the following probability distribution:
(i) K (ii) P (X < 3)
(iii) P (X > 6) (iv) P (0 < X < 3)
Find the probability of throwing at most 2 sixes in 6 throws of a single dieMathematics - Board Papers
How many times must a man toss a fair coin, so that the probability of having at least one head is more than 80%?Mathematics - Board Papers
A card from a pack of 52 playing cards is lost. From the remaining cards of the pack three cards are drawn at random (without replacement) and are found to be all spades. Find the probability of the lost card being a spade.
From a lot of 15 bulbs which include 5 defectives, a sample of 4 bulbs is drawn one by one with replacement. Find the probability distribution of number of defective bulbs. Hence find the mean of the distribution.Mathematics - Board Papers
An experiment succeeds thrice as often as it fails. Find the probability that in the next five trials, there will be at least 3 successes.Mathematics - Board Papers
A bag A contains 4 black and 6 red balls and bag B contains 7 black and 3 red balls. A die is thrown. If 1 or 2 appears on it, then bag A is chosen, otherwise bag B. If two balls are drawn at random (without replacement) from the selected bag, find the probability of one of them being red and another black.
An unbiased coin is tossed 4 times. Find the mean and variance of the number of heads obtained.Mathematics - Board Papers
On a multiple choice examination with three possible answers (out of which only one is correct) for each of the five questions, what is the probability that a candidate would get four or more correct answers just by guessing?Mathematics - Board Papers