## Question

Find the probability distribution of X, the number of heads in two tosses of a coin (or a simultaneous toss of two coin)

### Solution

When two coins are tossed, there may be 1 head, 2 heads or no head at all.

Thus, the possible values of X are 0, 1, 2,

Now,

P(X = 0) = P(getting no head) = P(TT) =

P(X = 1) = P(getting one head)

= P(HT or TH)

P(X = 2) = P(getting two heads) = P(HH) =

Thus, the required probability distribution of X is given by

#### SIMILAR QUESTIONS

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

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

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 *x*^{2} + *bx* + *c* > 0 for all *x* Ïµ **R** is

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

If two events *A* and *B* are such that *P*(*A ^{C}*) = 0.3,

*P*(

*B*) = 0.4 and

*P*(

*AB*) = 0.5 then

^{C}*P*(

*B/A*

*∪*

*B*) =

^{C}
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

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?

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?

Four bad oranges are mixed accidently with 16 good oranges. Find the probability distribution of the number of bad oranges in a draw of oranges.

Two dice are thrown simultaneously. If X denotes the number of sixes, find the expectation of X.