Let X denotes the number of heads in a single toss of 4 fair coins,
Match List I with List II.
|
LIST I |
LIST II |
|
A. Probability for X = 3 |
I. 2 |
|
B. Mathematical expectation of X |
II. 5 |
|
C. Value of E(X2) is |
III. 0.63 |
|
D. P(1 < X ≤ 3) is |
IV. 0.25 |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → A-IV, B-I, C-II, D-III
$X \sim \text{Binomial}(n=4,\; p=\frac{1}{2})$
$\text{(A)}\; P(X=3)=\frac{4!}{3!1!}\left(\frac{1}{2}\right)^4=\frac{4}{16}=0.25 \Rightarrow \text{(IV)}$
$\text{(B)}\; E(X)=np=4\cdot\frac{1}{2}=2 \Rightarrow \text{(I)}$
$\text{(C)}\; E(X^2)=npq+(np)^2=4\cdot\frac{1}{2}\cdot\frac{1}{2}+2^2=1+4=5 \Rightarrow \text{(II)}$
$\text{(D)}\; P(1\le X \le3)=P(2)+P(3)=\frac{6}{16}+\frac{4}{16}=\frac{10}{16}=0.625\approx0.63 \Rightarrow \text{(III)}$
A–IV,\; B–I,\; C–II,\; D–III