alleryStart learning →If $f(x) = kx^2(1 - x)$ for $0 < x < 1$ is the p.d.f. of $X$, the value of $k$ is:
- 10
- 12
- 6
- 8
Show answer and solution
Correct answer: B. 12
$\int_0^1 k(x^2 - x^3)\,dx = k[x^3/3 - x^4/4]_0^1 = k(1/3 - 1/4) = k/12 = 1$ ⇒ $k = 12$.
Indian Navy 10+2 B.Tech Cadet Probability & Statistics — practice questions
Explore 77 free Probability & Statistics questions in Indian Navy 10+2 B.Tech Cadet Mathematics. Open each question or exercise to read its content, reference answers and available explanation.
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Showing questions 1–30 of 77.
If $f(x) = kx^2(1 - x)$ for $0 < x < 1$ is the p.d.f. of $X$, the value of $k$ is:Read the answer and worked solution →Probability of a certain event:Read the answer and worked solution →For two events A and B, P(A | B) = 0.6, P(B) = 0.5, P(A) = 0.4. P(B | A) =Read the answer and worked solution →The probability of drawing a king from a standard pack of 52 cards is:Read the answer and worked solution →The probability of getting a number greater than 4 on a single throw of a die is:Read the answer and worked solution →The point dividing the segment from $(1,1)$ to $(4,7)$ in the ratio 1:2 is:Read the answer and worked solution →Find x such that the distance from (x, 1) to (2, 3) is √8.Read the answer and worked solution →The exact value of cos 60° is:Read the answer and worked solution →Sort each inverse function into its domainRead the answer and worked solution →Tap every function whose domain is [−1, 1]Read the answer and worked solution →Match each inverse function to its domainRead the answer and worked solution →Match each inverse function to its principal value branchRead the answer and worked solution →Flip and pair: function with its principal rangeRead the answer and worked solution →Which principal ranges sit around zero, and which run 0 to π?Read the answer and worked solution →Tap every function whose principal range has a point removedRead the answer and worked solution →Name the principal value branchRead the answer and worked solution →Domain checkRead the answer and worked solution →Put the reasoning in order: why an inverse needs a restricted domainRead the answer and worked solution →True or false: existence of inversesRead the answer and worked solution →True or false: reading the tableRead the answer and worked solution →Spot the one that does not belongRead the answer and worked solution →Two are true, one is notRead the answer and worked solution →Assertion and reasonRead the answer and worked solution →Complete the summary tableRead the answer and worked solution →Complete the rule about restricting a domainRead the answer and worked solution →Three of these are wrong. Find the one that holds.Read the answer and worked solution →Principal values worked in the chapterRead the answer and worked solution →Order the steps for finding a principal valueRead the answer and worked solution →True or false: principal valuesRead the answer and worked solution →Match each identity to the condition it needsRead the answer and worked solution →
Worked practice questions
Probability of a certain event:
- 0
- 1
- 1/2
- Negative
Show answer and solution
Correct answer: B. 1
P(certain event) = 1. P(impossible event) = 0. Probabilities lie in [0, 1].
Sum over all mutually exclusive complete outcomes = 1.
For two events A and B, P(A | B) = 0.6, P(B) = 0.5, P(A) = 0.4. P(B | A) =
- 0.75
- 0.4
- 0.5
- 0.6 × 0.5 / 0.4 = 0.75 (Bayes)
Show answer and solution
Correct answer: D. 0.6 × 0.5 / 0.4 = 0.75 (Bayes)
We have P(B|A) = P(A|B) × P(B)/P(A).
That is P(B|A) = 0.6 × 0.5 / 0.4.
So P(B|A) = 0.75.
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