Refer to the following Probability distribution table:
| \( X \) | 0 | 1 | 2 | 3 | 4 |
| P(X) | M | 6M | 0.1 | 0.1 | 0.1 |
Which of the following are TRUE ?
(A). \( P(0)=0.1 \)
(B). \( P(1)=0.7 \)
(C). \( P(X\lt 2)=0.7 \)
(D). \( P(X\gt 2)=0.2 \)
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → (A), (C) and (D) only
The probabilities add up to 1:
\( M+6M+0.1+0.1+0.1=1 \)
\( 7M=0.7 \)
\( M=0.1 \)
So \( P(0)=0.1 \), \( P(1)=0.6 \), \( P(X\lt 2)=0.1+0.6=0.7 \) and \( P(X\gt 2)=0.1+0.1=0.2 \).
Checking the statements
(A) \( P(0)=0.1 \) — Correct. \( P(0)=M=0.1 \).
(B) \( P(1)=0.7 \) — Incorrect. \( P(1)=6M=0.6 \).
(C) \( P(X\lt 2)=0.7 \) — Correct. \( P(0)+P(1)=0.1+0.6=0.7 \).
(D) \( P(X\gt 2)=0.2 \) — Correct. \( P(3)+P(4)=0.1+0.1=0.2 \).