Answer:
![Probability = \frac{1}{9}](https://tex.z-dn.net/?f=Probability%20%3D%20%5Cfrac%7B1%7D%7B9%7D)
Step-by-step explanation:
Given
Toppings: Pico de gallo, Onions and Steak
Required
The probability of getting Onions and Steak
The probability is calculated using:
--- because the events are independent
![P(Onion) = \frac{n(Onion)}{Total}](https://tex.z-dn.net/?f=P%28Onion%29%20%3D%20%5Cfrac%7Bn%28Onion%29%7D%7BTotal%7D)
![P(Onion) = \frac{1}{3}](https://tex.z-dn.net/?f=P%28Onion%29%20%3D%20%5Cfrac%7B1%7D%7B3%7D)
![P(Steak) = \frac{n(Steak)}{Total}](https://tex.z-dn.net/?f=P%28Steak%29%20%3D%20%5Cfrac%7Bn%28Steak%29%7D%7BTotal%7D)
![P(Steak) = \frac{1}{3}](https://tex.z-dn.net/?f=P%28Steak%29%20%3D%20%5Cfrac%7B1%7D%7B3%7D)
So, we have:
![Probability = P(Onion)\ and\ P(Steak)](https://tex.z-dn.net/?f=Probability%20%3D%20P%28Onion%29%5C%20and%5C%20P%28Steak%29)
![Probability = P(Onion)\ *\ P(Steak)](https://tex.z-dn.net/?f=Probability%20%3D%20P%28Onion%29%5C%20%2A%5C%20P%28Steak%29)
![Probability = \frac{1}{3} * \frac{1}{3}](https://tex.z-dn.net/?f=Probability%20%3D%20%5Cfrac%7B1%7D%7B3%7D%20%2A%20%5Cfrac%7B1%7D%7B3%7D)
![Probability = \frac{1}{9}](https://tex.z-dn.net/?f=Probability%20%3D%20%5Cfrac%7B1%7D%7B9%7D)
Answer:
Step-by-step explanation:
Answer:
Shifted by 6 units left on the x-axis.
Step-by-step explanation:
Given function is,
f(x) = 5ˣ + 1
After transformation, this function becomes g(x) = ![5^{(x+6)}+1](https://tex.z-dn.net/?f=5%5E%7B%28x%2B6%29%7D%2B1)
Here, g(x) = f(x + 6)
By the rule of transformation,
Function 'f' has been shifted by 6 units left on the x-axis to form a new function 'g'.
Answer:
The probability that the 3rd defective mirror is the 10th mirror examined = 0.0088
Step-by-step explanation:
Given that:
Probability of manufacturing a defective mirror = 0.075
To find the probability that the 3rd defective mirror is the 10th mirror examined:
Let X be the random variable that follows a negative Binomial expression.
Then;
![X \sim -ve \ Bin (k = 3 , p = 0.075)\\ \\ P(X=x)= \bigg (^{x-1}_{k-1}\bigg)\times P^k\times (1-P)^{x-k}](https://tex.z-dn.net/?f=X%20%5Csim%20%20-ve%20%20%5C%20Bin%20%28k%20%3D%203%20%2C%20p%20%3D%200.075%29%5C%5C%20%5C%5C%20P%28X%3Dx%29%3D%20%5Cbigg%20%28%5E%7Bx-1%7D_%7Bk-1%7D%5Cbigg%29%5Ctimes%20P%5Ek%5Ctimes%20%281-P%29%5E%7Bx-k%7D)
![= \bigg (^{10-1}_{3-1}\bigg)\times 0.075^3\times (1-0.075)^{10-3}](https://tex.z-dn.net/?f=%3D%20%5Cbigg%20%28%5E%7B10-1%7D_%7B3-1%7D%5Cbigg%29%5Ctimes%200.075%5E3%5Ctimes%20%281-0.075%29%5E%7B10-3%7D)
![= \bigg (^9_2\bigg)\times 0.075^3\times (1-0.075)^{7}](https://tex.z-dn.net/?f=%3D%20%5Cbigg%20%28%5E9_2%5Cbigg%29%5Ctimes%200.075%5E3%5Ctimes%20%281-0.075%29%5E%7B7%7D)
![= \dfrac{9!}{2!(9-2)!}\times 0.075^3\times (0.925)^{7}](https://tex.z-dn.net/?f=%3D%20%5Cdfrac%7B9%21%7D%7B2%21%289-2%29%21%7D%5Ctimes%200.075%5E3%5Ctimes%20%280.925%29%5E%7B7%7D)
![= \dfrac{9*8*7!}{2!(7)!}\times 0.075^3\times (0.925)^{7}](https://tex.z-dn.net/?f=%3D%20%5Cdfrac%7B9%2A8%2A7%21%7D%7B2%21%287%29%21%7D%5Ctimes%200.075%5E3%5Ctimes%20%280.925%29%5E%7B7%7D)
= 0.0087999
≅ 0.0088