Answer:
The probability that all are male of choosing '3' students
P(E) = 0.067 = 6.71%
Step-by-step explanation:
Let 'M' be the event of selecting males n(M) = 12
Number of ways of choosing 3 students From all males and females
![n(M) = 28C_{3} = \frac{28!}{(28-3)!3!} =\frac{28 X 27 X 26}{3 X 2 X 1 } = 3,276](https://tex.z-dn.net/?f=n%28M%29%20%3D%2028C_%7B3%7D%20%3D%20%5Cfrac%7B28%21%7D%7B%2828-3%29%213%21%7D%20%3D%5Cfrac%7B28%20X%2027%20X%2026%7D%7B3%20X%202%20X%201%20%7D%20%3D%203%2C276)
Number of ways of choosing 3 students From all males
![n(M) = 12C_{3} = \frac{12!}{(12-3)!3!} =\frac{12 X 11 X 10}{3 X 2 X 1 } =220](https://tex.z-dn.net/?f=n%28M%29%20%3D%2012C_%7B3%7D%20%3D%20%5Cfrac%7B12%21%7D%7B%2812-3%29%213%21%7D%20%3D%5Cfrac%7B12%20X%2011%20X%2010%7D%7B3%20X%202%20X%201%20%7D%20%3D220)
The probability that all are male of choosing '3' students
![P(E) = \frac{n(M)}{n(S)} = \frac{12 C_{3} }{28 C_{3} }](https://tex.z-dn.net/?f=P%28E%29%20%3D%20%5Cfrac%7Bn%28M%29%7D%7Bn%28S%29%7D%20%3D%20%5Cfrac%7B12%20C_%7B3%7D%20%7D%7B28%20C_%7B3%7D%20%7D)
![P(E) = \frac{12 C_{3} }{28 C_{3} } = \frac{220}{3276}](https://tex.z-dn.net/?f=P%28E%29%20%3D%20%20%5Cfrac%7B12%20C_%7B3%7D%20%7D%7B28%20C_%7B3%7D%20%7D%20%3D%20%5Cfrac%7B220%7D%7B3276%7D)
P(E) = 0.067 = 6.71%
<u><em>Final answer</em></u>:-
The probability that all are male of choosing '3' students
P(E) = 0.067 = 6.71%
Answer:
1/10.
Step-by-step explanation:
Prob(Spinning a 1) = 1/5.
Prob(Flipping a Head) = 1/2.
Probability of a 1 then a head = 1/5 * 1/2 = 1/10.
Note: we multiply the probabilities because the 2 events are independent.
0.3(3 - 0.5)
= 0.3(2.5)
= 0.75
Answer:
![$(10, 0)$](https://tex.z-dn.net/?f=%24%2810%2C%200%29%24)
Step-by-step explanation:
Let's try all the options:
![$\left \{ {{2x + y = 20} \atop {4x-2y = 40} \right. $](https://tex.z-dn.net/?f=%24%5Cleft%20%5C%7B%20%7B%7B2x%20%2B%20y%20%3D%2020%7D%20%5Catop%20%7B4x-2y%20%3D%2040%7D%20%5Cright.%20%24)
Considering
:
![$\left \{ {{2(10) + 0 = 20} \atop {4(10)-2(0) = 40} \right. $\\](https://tex.z-dn.net/?f=%24%5Cleft%20%5C%7B%20%7B%7B2%2810%29%20%2B%200%20%3D%2020%7D%20%5Catop%20%7B4%2810%29-2%280%29%20%3D%2040%7D%20%5Cright.%20%24%5C%5C)
![$\left \{ {{20 + 0 = 20} \atop {40-0 = 40} \right. $](https://tex.z-dn.net/?f=%24%5Cleft%20%5C%7B%20%7B%7B20%20%2B%200%20%3D%2020%7D%20%5Catop%20%7B40-0%20%3D%2040%7D%20%5Cright.%20%24)
![$\left \{ {{20= 20} \atop {40 = 40} \right. $](https://tex.z-dn.net/?f=%24%5Cleft%20%5C%7B%20%7B%7B20%3D%2020%7D%20%5Catop%20%7B40%20%3D%2040%7D%20%5Cright.%20%24)
Considering
:
![$\left \{ {{2(0) + 10 = 20} \atop {4(0)-2(10) = 40} \right. $\\](https://tex.z-dn.net/?f=%24%5Cleft%20%5C%7B%20%7B%7B2%280%29%20%2B%2010%20%3D%2020%7D%20%5Catop%20%7B4%280%29-2%2810%29%20%3D%2040%7D%20%5Cright.%20%24%5C%5C)
![$\left \{ {{0 + 10 = 20} \atop {0-20 = 40} \right. $](https://tex.z-dn.net/?f=%24%5Cleft%20%5C%7B%20%7B%7B0%20%2B%2010%20%3D%2020%7D%20%5Catop%20%7B0-20%20%3D%2040%7D%20%5Cright.%20%24)
![$\left \{ {{10= 20} \atop {-20 = 40} \right. $](https://tex.z-dn.net/?f=%24%5Cleft%20%5C%7B%20%7B%7B10%3D%2020%7D%20%5Catop%20%7B-20%20%3D%2040%7D%20%5Cright.%20%24)
![$\left \{ {{10\neq 20} \atop {-20 \neq 40} \right. $](https://tex.z-dn.net/?f=%24%5Cleft%20%5C%7B%20%7B%7B10%5Cneq%20%2020%7D%20%5Catop%20%7B-20%20%5Cneq%2040%7D%20%5Cright.%20%24)
Considering
:
![$\left \{ {{2(4) + 2 = 20} \atop {4(4)-2(2) = 40} \right. $\\](https://tex.z-dn.net/?f=%24%5Cleft%20%5C%7B%20%7B%7B2%284%29%20%2B%202%20%3D%2020%7D%20%5Catop%20%7B4%284%29-2%282%29%20%3D%2040%7D%20%5Cright.%20%24%5C%5C)
![$\left \{ {{8 + 2 = 20} \atop {8-4 = 40} \right. $](https://tex.z-dn.net/?f=%24%5Cleft%20%5C%7B%20%7B%7B8%20%2B%202%20%3D%2020%7D%20%5Catop%20%7B8-4%20%3D%2040%7D%20%5Cright.%20%24)
![$\left \{ {{10= 20} \atop {4 = 40} \right. $](https://tex.z-dn.net/?f=%24%5Cleft%20%5C%7B%20%7B%7B10%3D%2020%7D%20%5Catop%20%7B4%20%3D%2040%7D%20%5Cright.%20%24)
![$\left \{ {{10\neq 20} \atop {4 \neq 40} \right. $](https://tex.z-dn.net/?f=%24%5Cleft%20%5C%7B%20%7B%7B10%5Cneq%20%2020%7D%20%5Catop%20%7B4%20%5Cneq%20%2040%7D%20%5Cright.%20%24)
Considering
:
![$\left \{ {{2(10) -10 = 20} \atop {4(10)-2(-10) = 40} \right. $\\](https://tex.z-dn.net/?f=%24%5Cleft%20%5C%7B%20%7B%7B2%2810%29%20-10%20%3D%2020%7D%20%5Catop%20%7B4%2810%29-2%28-10%29%20%3D%2040%7D%20%5Cright.%20%24%5C%5C)
![$\left \{ {{20 -10 = 20} \atop {40+20 = 40} \right. $](https://tex.z-dn.net/?f=%24%5Cleft%20%5C%7B%20%7B%7B20%20-10%20%3D%2020%7D%20%5Catop%20%7B40%2B20%20%3D%2040%7D%20%5Cright.%20%24)
![$\left \{ {{10= 20} \atop {60 = 40} \right. $](https://tex.z-dn.net/?f=%24%5Cleft%20%5C%7B%20%7B%7B10%3D%2020%7D%20%5Catop%20%7B60%20%3D%2040%7D%20%5Cright.%20%24)
![$\left \{ {{10\neq 20} \atop {60 \neq 40} \right. $](https://tex.z-dn.net/?f=%24%5Cleft%20%5C%7B%20%7B%7B10%5Cneq%20%2020%7D%20%5Catop%20%7B60%20%5Cneq%20%2040%7D%20%5Cright.%20%24)