(i) For two tosses of a coin the sample space is {HH, HT, TH, TT}
Let X denote the number of heads in two tosses of a coin.
Then X can take values 0, 1, 2.
∴ P[X = 0] = P(0) = 1/4
P[X = 1] = P(1) = 2/4 = 1/2
P[X = 2] = P(2) = 1/4
∴ the required probability distribution is
| X = x |
0 |
1 |
2 |
| P(X = x) |
1/4 |
1/2 |
1/4 |
(ii) When three coins are tossed simultaneously, then the sample space is
{HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}
Let X denotes the number of tails.
Then X can take the value 0, 1, 2, 3.
∴ P[X = 0] = P(0) = 1/8
P[X = 1] = P(1) = 3/8
P[X = 2] = P(2) = 3/8
P[X = 3] = P(3) = 1/8
∴ the required probability distribution is
| X = x |
0 |
1 |
2 |
3 |
| P(X = x) |
1/8 |
3/8 |
3/8 |
1/8 |
(iii) When a fair coin is tossed 4 times, then the sample space is
S = {HHHH, HHHT, HHTH, HTHH, THHH, HHTT, HTHT, HTTH, THHT, THTH, TTHH, HTTT, THTT, TTHT, TTTH, TTTT}
∴ n(S) = 16
Let X denotes the number of heads.
Then X can take the value 0, 1, 2, 3, 4
When X = 0, then X = {TTTT}
∴ n(X) = 1
∴ P(X = 0) = \(\frac{n(X)}{n(S)}\) = 1/16
When X = 1, then
X = {HTTT, THTT, TTHT, TTTH}
∴ n(X) = 4
When X = 2, then
X = {HHTT, HTHT, HTTH, THHT, THTH, TTHH}
∴ n(X) = 6
When X = 3, then
X = {HHHT, HHTH, HTHH, THHH}
∴ n(X) = 4
When X = 4, then X = {HHHH}
∴ n(X) = 1
∴ the probability distribution of X is as follows :
| X = x |
0 |
1 |
2 |
3 |
4 |
| P(X = x) |
1/16 |
1/4 |
3/8 |
1/4 |
1/16 |
