A coin is tossed 3 times. If X denotes the number of heads, then Match List I with List II.
|
LIST I |
LIST II |
|
A. P(X = 0) |
I. $\frac{1}{8}$ |
|
B. P(X = 1) |
II. $\frac{7}{8}$ |
|
C. P(X ≤ 2) |
III. $\frac{4}{8}$ |
|
D. P(X ≥ 2) |
IV. $\frac{3}{8}$ |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) - A-I, B-IV, C-II, D-III
(A) $P(X = 0)={^3C}_0×(\frac{1}{2})^3=\frac{1}{8}$ (I)
(B) $P(X = 1)={^3C}_1×(\frac{1}{2})×(\frac{1}{2})^2=\frac{3}{8}$ (IV)
(C) $P(X ≤ 2)=1-P(X=3)$
$=1-{^3C}_3(\frac{1}{2})^3=\frac{7}{8}$ (II)
(D) $P(X ≥ 2)=P(X=2)+P(X=3)$
$={^3C}_2(\frac{1}{2})^3+{^3C}_3(\frac{1}{2})^3=\frac{4}{8}$ (III)