A die numbered $1$ - $6$ is rolled $100$ times and the results are recorded in a table.
$1$
$2$
$3$
$4$
$5$
$6$
$18$
$9$
$8$
$16$
$37$
$12$
Find the probability of getting $5$ .

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Solution

Let's find the probability of getting $5$ :
Probability of an outcome, $P (O)$ $= \frac{t h e n u m b e r o f t i m e s t h e f a v o u r a b l e o u t c o m e o c c u r s}{t h e t o t a l n u m b e r o f t i m e s t h e e x p e r i m e n t i s d o n e}$
The total number of times the outcome is $5$ $= 37$
The total number of times the die is rolled $= 100$
$P (5)$ $= \frac{37}{100}$

Hence, the probability of getting $5$ is $\frac{37}{100}$ .

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Verify the following :

(i) $\frac{3}{7} \times (\frac{5}{6} + \frac{12}{13}) = (\frac{3}{7} \times \frac{5}{6}) + (\frac{3}{7} \times \frac{12}{13})$
(ii) $\frac{- 15}{4} \times (\frac{3}{7} + \frac{- 12}{5}) = (\frac{- 15}{4} \times \frac{3}{7}) + (\frac{- 15}{4} \times \frac{- 12}{5})$
(iii) $(\frac{- 8}{3} + \frac{- 13}{12}) \times \frac{5}{6} = (\frac{- 8}{3} \times \frac{5}{6}) + (\frac{- 13}{12} \times \frac{5}{6})$
(iv) $\frac{- 16}{7} \times (\frac{- 8}{9} + \frac{- 7}{6}) = (\frac{- 16}{7} \times \frac{- 8}{9}) + (\frac{- 16}{7} \times \frac{- 7}{6})$

Prove that:
(i) $\frac{1}{3 + \sqrt{7}} + \frac{1}{\sqrt{7} + \sqrt{5}} + \frac{1}{\sqrt{5} + \sqrt{3}} + \frac{1}{\sqrt{3} + 1} = 1$
(ii) $\frac{1}{1 + \sqrt{2}} + \frac{1}{\sqrt{2} + \sqrt{3}} + \frac{1}{\sqrt{3} + \sqrt{4}} + \frac{1}{\sqrt{4} + \sqrt{5}} + \frac{1}{\sqrt{5} + \sqrt{6}} + \frac{1}{\sqrt{6} + \sqrt{7}} + \frac{1}{\sqrt{7} + \sqrt{8}} + \frac{1}{\sqrt{8} + \sqrt{9}} = 2$

If A = {3, 6, 9, 12, 15, 18, 21}
B = {2, 4, 6, 8, 10, 12, 14, 16}
C = {5, 10, 15, 20}

$\begin{matrix} A & B 1. B - C & A . {5, 10, 20} 2. A - C & B . {3, 9, 15, 21} 3. C - (A - B) & C . {3, 6, 9, 12, 18, 21} 4. C \cap (A - B) & D . {15} E . {2, 4, 6, 8, 12, 14, 16} \end{matrix}$

The mean of the data 2, 8, 6, 5, 4, 5, 6, 3, 6, 4, 9, 1, 5, 6, 5 is given to be 5. Based on this information, is it correct to say that the mean of the data 10, 12, 10, 2, 18, 8, 12, 6, 12, 10, 8, 10, 12, 16, 4 is 10? Give reason.

Q. If set A = {4, 6, 8, 10, 12}, set B = {3, 6, 9, 12, 15, 18} and set C = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, then find A ∩ C.

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A die numbered 1 - 6 is rolled 100 times and the results are recorded in a table. 1234561898163712 Find the probability of getting 5.

A die numbered $1$ - $6$ is rolled $100$ times and the results are recorded in a table.
$1$
$2$
$3$
$4$
$5$
$6$
$18$
$9$
$8$
$16$
$37$
$12$
Find the probability of getting $5$ .