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The letters of the word STORY be arranged randomly. Find the probability that
a) T and Y are together.
b) arrangment begins with T and end with Y.
a) T and Y are together.
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Two dice are thrown together. What is the probability that,
i) Sum of the numbers is divisible by 3 or 4?
ii) Sum of the numbers is neither divisible by 3 nor 5?
i) Sum of the numbers is divisible by 3 or 4?
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$\frac{x^2}{4}-\frac{y^2}{12}=1$
$\frac{y^2}{9}-\frac{x^2}{16}=1$
→$\frac{x^2}{4}-\frac{y^2}{12}=1$
$\frac{y^2}{9}-\frac{x^2}{16}=1$
If $A$ and $B$ are two independent events and $P(A)=\frac{3}{5}, P(B)=\frac{2}{3}$, find
i) $\mathrm{P}(\mathrm{A} \cap \mathrm{B})$ ii) $\mathrm{P}\left(\mathrm{A}^{\prime} \cap \mathrm{B}^{\prime}\right)$ iii) $\mathrm{P}\left(\mathrm{A}^{\prime} \cap \mathrm{B}\right)$ iv) $P\left(A^{\prime} \cap B^{\prime}\right)$ v) $P(A \cup B)$
→i) $\mathrm{P}(\mathrm{A} \cap \mathrm{B})$ ii) $\mathrm{P}\left(\mathrm{A}^{\prime} \cap \mathrm{B}^{\prime}\right)$ iii) $\mathrm{P}\left(\mathrm{A}^{\prime} \cap \mathrm{B}\right)$ iv) $P\left(A^{\prime} \cap B^{\prime}\right)$ v) $P(A \cup B)$
If A∪B∪C = S (the sample space) and A, B and C are mutually exclusive events, can the
following represent probability assignment?
i) P(A) = 0.2, P(B) = 0.7, P(C) = 0.1
ii) P(A) = 0.4, P(B) = 0.6, P(C) = 0.2
following represent probability assignment?
i) P(A) = 0.2, P(B) = 0.7, P(C) = 0.1
ii) P(A) = 0.4, P(B) = 0.6, P(C) = 0.2
Suppose $f(x)=p x+3$ for $a \leq x \leq b$
$=5 x^2-q \text { for } b<x \leq c$
Find the condition on $p, q$, so that $f(x)$ is continuous on $[a, c]$, by filling in the boxes
→$=5 x^2-q \text { for } b<x \leq c$
Find the condition on $p, q$, so that $f(x)$ is continuous on $[a, c]$, by filling in the boxes
The marks scored in a test by seven randomly selected students are
Find the Variance and Standard Deviation of these seven students.
Find the Variance and Standard Deviation of these seven students.
The number of centuries scored in a year by seven randomly selected batsmen are
Find the Variance and Standard Deviation of these seven batsmen.
Find the Variance and Standard Deviation of these seven batsmen.