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 — practice questions
Explore 35 free Probability questions in Indian Navy 10+2 B.Tech Cadet Mathematics. Open each question or exercise to read its content, reference answers and available explanation.
Practise Probability with Quill →Probability questions and exercises with answers
Showing questions 1–30 of 35.
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 →Find mean of {2, 4, 6, 8, 10}:Read the answer and worked solution →P(drawing an Ace OR King from a deck) =Read the answer and worked solution →Number of ways to choose 3 students from a class of 10:Read the answer and worked solution →Standard deviation has the same units as: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 probability of getting a head when an unbiased coin is tossed once is:Read the answer and worked solution →Complete the definition of conditional probabilityRead the answer and worked solution →True or false: conditional probabilityRead the answer and worked solution →Independent or mutually exclusive?Read the answer and worked solution →Match each rule to its nameRead the answer and worked solution →IndependenceRead the answer and worked solution →Order the steps for a Bayes' theorem questionRead the answer and worked solution →Complete the conditions for a partitionRead the answer and worked solution →True or false: independence versus exclusivityRead the answer and worked solution →Assertion and reasonRead the answer and worked solution →Tap every statement that follows from independenceRead the answer and worked solution →The multiplication ruleRead 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 →Three of these are wrong. Find the one that holds.Read the answer and worked solution →Complete the theorem of total probabilityRead the answer and worked solution →Which theorem answers which question?Read the answer and worked solution →True or false: total probability and BayesRead the answer and worked solution →Match each historical figure to their contributionRead the answer and worked solution →The Historical NoteRead the answer and worked solution →Flip and pair: notation with meaningRead the answer and worked solution →Order the reasoning: from a partition to a posteriorRead 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.
Find mean of {2, 4, 6, 8, 10}:
- 5
- 6
- 7
- 8
Show answer and solution
Correct answer: B. 6
Sum = 30, n = 5. Mean = 30/5 = 6.
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