Question

In a game, a person is paid Rs. 5 if he gets all heats or all tails when three coin are tossed, and he will pay Rs. 3 if either one or two heads shown. What can be expect to win on the average per game?

Solution

Correct option is

- 1

Let X be the amount received by the person. Then, X can take values 5 and 3 such that P(X = 5) = probability of getting all heads of all tails when three coins are tossed.

        P(X = – 3) = probability or getting one or two heads

∴      Expected amount to win, on the average, per game

        

Thus, the person will on the average, lose Re 1 per toss of the coins.

SIMILAR QUESTIONS

Q1

A bag contains 2 Black, 4 white and 3 Red balls. One ball is drawn at random and kept aside. Then another ball is drawn and is also kept aside. This process is continued till all are drawn. Find the probability that the balls drawn are in the sequence 2 Black, 4 white and 3Red

Q2

If X follows a binomial distribution with parameters n = 100, p = 1/3, then P(X = r) is maximum when r =

Q3

A team of 8 couples, (husband and wife) attend a lucky draw in which 4 persons picked up for a prize. Then, the probability that there is at least one couple is

Q4

An unbiased die with faces marked 1, 2, 3, 4, 5 and 6 is rolled four times. Out of four face values obtained, the probability that the minimum face value is not less than 2 and the maximum face value is not greater than 5 is

Q5

If X following a binomial distribution with parameters n = 8 and p = 1/2, then  equals

Q6

Two numbers b and c are chosen at random with replacement from the numbers 1, 2, 3, 4, 5, 6, 7, 8 and 9. The probability that x2 + bx + c > 0 for all x Ïµ R is

Q7

India plays two matches each with west indies and Australia. In any one match, the probabilities of India getting points 0, 1, 2 are respectively 0.45, 0.05 and 0.05 and 0.50 for base drawn and won. Assuming that the outcomes are independent, the probability of India getting at least 7 points is

Q8

If two events A and B are such that P(AC) = 0.3, P(B) = 0.4 and P(ABC) = 0.5 then P(B/A  BC) =

Q9

A bag contains n + 1 coins. It is known that one of these coins shows heads on both sides, whereas the other coins are fair. One coin is selected at random and tossed. If the probability that toss results in heads is 7/12, then the value of n is

Q10

A salesman wants to know the average number of units he sells per sales call. He checks his past records and comes up with the following probabilities:

Sales (in units):

0

1

2

3

4

5

Probability:

0.15

0.20

0.10

0.05

0.30

0.20

What is the average number of units he sale call?