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andriy [413]
3 years ago
13

What is the probability of spinning a number less than 3 or6

Mathematics
1 answer:
Ipatiy [6.2K]3 years ago
8 0

Answer:

Probability of a dice rolling a number less than 3 is 2/6 = 1/3

Probability of dice spinning a number less than 6 is 5/6

Step-by-step explanation:

Number less than 3:

Chances of no. Being 1 and 2, not including 3, is 1/6 individually.

Hence, chances of no. Rolled being lesser than 3 is 1/6 + 1/6 = 1/3

Probability of no. Being smaller than 6 (lesser than 6) Aka spinning 1 or 2 or 3 or 4 or 5, not including 6 is (1/6) x 5 = 5/6

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<img src="https://tex.z-dn.net/?f=%20%5Cint%20%7Btan%7D%5E%7B3%7D%20x%20%5C%3A%20dx" id="TexFormula1" title=" \int {tan}^{3} x \
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\frac{ {tan}^{2}  x}{2}  +  \ln( |cos \: x| ) + C

Step-by-step explanation:

\int {tan}^{3} x \: dx

\int \: tan \: x \times  {tan}^{2} x \: dx

\int \: tan \: x( {sec}^{2} x - 1) \: dx

distribute

\int \: tan \: x  \: {sec}^{2} x - tan \: x \: dx

\int \: tan \: x \:  {sec}^{2} x  \: dx \:  - \int \: tan \: x \: dx

\int \: tan \: x \:  {sec}^{2} x  \: dx \:  - \int \frac{sin \: x}{cos \: x} \: dx

<u>F</u><u>i</u><u>r</u><u>s</u><u>t</u><u> </u><u>i</u><u>n</u><u>t</u><u>e</u><u>g</u><u>r</u><u>a</u><u>n</u><u>d</u>

let tan x = u

du = sec²x dx

<u>S</u><u>e</u><u>c</u><u>o</u><u>n</u><u>d</u><u> </u><u>i</u><u>n</u><u>t</u><u>e</u><u>g</u><u>r</u><u>a</u><u>n</u><u>d</u>

let cos x = z

dz = -sin x dx

= \int u \: du \:   -  \int -  \frac{1}{z} dz

=  \frac{ {u}^{2} }{2}   +  \ln( |z| )  + C

=  \color{red}{ \boxed{ \frac{ {tan}^{2}  x}{2}  +  \ln( |cos \: x| ) + C}}

7 0
3 years ago
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