Question:
A student studies for (X) number of hours during a randomly selected school day. The probability that (X) can take the values, has the following form, where (k) is some constant.
(P(X = x) =
0.2, & if x = 0
kx, & if x = 1 or 2
k(6 - x), & if x = 3 or 4
0, & otherwise
)
The probability that the student studies for at most two hours is
A student studies for (X) number of hours during a randomly selected school day. The probability that (X) can take the values, has the following form, where (k) is some constant.
(P(X = x) = 0.2, & if x = 0
kx, & if x = 1 or 2
k(6 - x), & if x = 3 or 4
0, & otherwise )
The probability that the student studies for at most two hours is
(P(X = x) = 0.2, & if x = 0
kx, & if x = 1 or 2
k(6 - x), & if x = 3 or 4
0, & otherwise )
The probability that the student studies for at most two hours is
Show Hint
Always sum all possible probabilities to 1 to find the unknown constant $k$.
Updated On: Apr 30, 2026
- (0.1)
- (0.5)
- (0.3)
- [suspicious link removed]
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The Correct Option is B
Solution and Explanation
Step 1: Find $k$
Sum of probabilities $= 1$.
$P(0) + P(1) + P(2) + P(3) + P(4) = 1$.
$0.2 + k(1) + k(2) + k(6-3) + k(6-4) = 1$.
$0.2 + k + 2k + 3k + 2k = 1 \implies 0.2 + 8k = 1 \implies 8k = 0.8 \implies k = 0.1$.
Step 2: Calculate $P(X \le 2)$
$P(X \le 2) = P(0) + P(1) + P(2)$.
$P(X \le 2) = 0.2 + (0.1)(1) + (0.1)(2) = 0.2 + 0.1 + 0.2 = 0.5$.
Final Answer: (B)
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