Answer: 0.0187
Step-by-step explanation:
The binomial distribution formula for probability :-
, where P(x) is the probability of getting success in x trials , n is the total number of trials and p is the probability of getting success in each trial.
Given : The probability that the physics majors belong to ethnic minorities =0.33
Number of students selected : n= 8
Now, the probability that more than 5 belong to an ethnic minority :-
![P(x>5)=P(6)+P(7)+P(8)\\\\=^8C_6(0.33)^6(0.67)^{2}+^8C_7(0.33)^7(0.67)^{1}+^8C_8(0.33)^8(0.67)^{0}\\\\=(\dfrac{8!}{6!2!})(0.33)^6(0.67)^{2}+(8)(0.33)^7(0.67)^{1}+(0.33)^8(0.67)^{0}\\\\=0.0186577086013\approx0.0187](https://tex.z-dn.net/?f=P%28x%3E5%29%3DP%286%29%2BP%287%29%2BP%288%29%5C%5C%5C%5C%3D%5E8C_6%280.33%29%5E6%280.67%29%5E%7B2%7D%2B%5E8C_7%280.33%29%5E7%280.67%29%5E%7B1%7D%2B%5E8C_8%280.33%29%5E8%280.67%29%5E%7B0%7D%5C%5C%5C%5C%3D%28%5Cdfrac%7B8%21%7D%7B6%212%21%7D%29%280.33%29%5E6%280.67%29%5E%7B2%7D%2B%288%29%280.33%29%5E7%280.67%29%5E%7B1%7D%2B%280.33%29%5E8%280.67%29%5E%7B0%7D%5C%5C%5C%5C%3D0.0186577086013%5Capprox0.0187)
Hence, the probability that more than 5 belong to an ethnic minority = 0.0187
Answer: 1,341 3/4
Step-by-step explanation:
Answer:
(2, 7 )
Step-by-step explanation:
Given the 2 equations
y = 2x + 3 → (1)
y = 3x + 1 → (2)
Substitute y = 3x + 1 into (1)
3x + 1 = 2x + 3 ( subtract 2x from both sides )
x + 1 = 3 ( subtract 1 from both sides )
x = 2
Substitute x = 2 into either of the 2 equations for corresponding value of y
Substituting x = 2 into (1)
y = 2(2) + 3 = 4 + 3 = 7
Solution is (2, 7 )
4 to 7......add them = 11
4/11 * 33 = 132/11 = 12
7/11 * 33 = 231/11 = 21
The probability to choose letter n is
![\frac{1}{26}](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B26%7D%20)
. After drawing letter n there left 25 letters and the probability to choose the letter w is
![\frac{1}{25}](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B25%7D%20)
. After drawing two letters n and w there left 24 letters and then the probability to choose letter b is
![\frac{1}{24}](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B24%7D%20)
. After drawing three letters n, w and b there left 23 letters, so the probability to choose letter t is
![\frac{1}{23}](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B23%7D%20)
.
Using the product rule for probabilities, you can obtain that
![P= \frac{1}{26} * \frac{1}{25} * \frac{1}{24}* \frac{1}{23} =0.0000027](https://tex.z-dn.net/?f=P%3D%20%5Cfrac%7B1%7D%7B26%7D%20%2A%20%5Cfrac%7B1%7D%7B25%7D%20%2A%20%5Cfrac%7B1%7D%7B24%7D%2A%20%5Cfrac%7B1%7D%7B23%7D%20%3D0.0000027)
.