A coin is tossed until a head appears or the tail appears 4 times in succession. Find the probability distribution of the number of tosses.
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) →
|
$X$ |
0 |
1 |
2 |
3 |
|
$P(X)$ |
$\frac{1}{2}$ |
$\frac{1}{4}$ |
$\frac{1}{8}$ |
$\frac{1}{8}$ |
The sample space associated with this experiment is
$S = \{H, TH, TTH, TTTH, TTTT\}$
Let the random variable X be defined as the number of tosses. Then X can take the values 1, 2, 3, 4. The corresponding probabilities are
$P(X = 1) = P(H)=\frac{1}{2}$
$P(X = 2) = P(TH)=\frac{1}{4}$
$P(X = 3)= P(TTH)=\frac{1}{8}$
$P(X = 4) = P(TTTH, TTTT)=\frac{1}{8}$
We observe that $ΣP(X)=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{8}=1$
The probability distribution of the number of tosses is
|
$X$ |
0 |
1 |
2 |
3 |
|
$P(X)$ |
$\frac{1}{2}$ |
$\frac{1}{4}$ |
$\frac{1}{8}$ |
$\frac{1}{8}$ |