Let X denotes the number of hours you study during a randomly selected school day. The random variable X has the following probability distribution.
|
X |
0 |
1 |
2 |
3 |
4 |
|
P(X) |
K |
2K |
2K |
2K |
K |
Match List – I with List – II.
|
List - I |
List - II |
|
(A) Value of K |
(I) $\frac{1}{4}$ |
|
(B) Probability you study at least two hours |
(II) $\frac{1}{8}$ |
|
(C) Probability you study exactly two hours |
(III) $\frac{3}{8}$ |
|
(D) Probability you study at most one hour |
(IV) $\frac{5}{8}$ |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → (A)-(II), (B)-(IV), (C)-(I), (D)-(III)
$∑P(X)=1⇒(k+2k+2k+2k+k)=1$
$⇒8k=1⇒k=\frac{1}{8}$
A. $k=\frac{1}{8}$ (II)
B. $P(X≥2)=5k=\frac{5}{8}$ (IV)
C. $P(X=2)=2k=\frac{1}{4}$ (I)
D. $P(X≤2)=3k=\frac{3}{8}$ (III)