Answer:
![\sf \dfrac{1}{7}](https://tex.z-dn.net/?f=%5Csf%20%5Cdfrac%7B1%7D%7B7%7D)
Step-by-step explanation:
Given labeled tiles: B, C, D, E, F, G, H
Total number of tiles = 7
Vowels = A, E, I, O and U
⇒ Total number of vowel tiles in bag = 1
![\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}](https://tex.z-dn.net/?f=%5Csf%20Probability%5C%3Aof%5C%3Aan%5C%3Aevent%5C%3Aoccurring%20%3D%20%5Cdfrac%7BNumber%5C%3Aof%5C%3Aways%5C%3Ait%5C%3Acan%5C%3Aoccur%7D%7BTotal%5C%3Anumber%5C%3Aof%5C%3Apossible%5C%3Aoutcomes%7D)
![\implies \sf Probability\:of\:picking\:a\:vowel= \dfrac{Number\:of\:vowel\:tiles}{Total\:number\:of\:tiles}=\dfrac{1}{7}](https://tex.z-dn.net/?f=%5Cimplies%20%5Csf%20Probability%5C%3Aof%5C%3Apicking%5C%3Aa%5C%3Avowel%3D%20%5Cdfrac%7BNumber%5C%3Aof%5C%3Avowel%5C%3Atiles%7D%7BTotal%5C%3Anumber%5C%3Aof%5C%3Atiles%7D%3D%5Cdfrac%7B1%7D%7B7%7D)
Answer:
31.77% probability the surgery is successful for exactly five patients.
Step-by-step explanation:
For each patient, there are only two possible outcomes. Either the surgery is successful, or it is not. The probability of the surgery being successful for a patient is independent of other patients. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
![P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}](https://tex.z-dn.net/?f=P%28X%20%3D%20x%29%20%3D%20C_%7Bn%2Cx%7D.p%5E%7Bx%7D.%281-p%29%5E%7Bn-x%7D)
In which
is the number of different combinations of x objects from a set of n elements, given by the following formula.
![C_{n,x} = \frac{n!}{x!(n-x)!}](https://tex.z-dn.net/?f=C_%7Bn%2Cx%7D%20%3D%20%5Cfrac%7Bn%21%7D%7Bx%21%28n-x%29%21%7D)
And p is the probability of X happening.
A surgical technique is performed on seven patients.
This means that ![n = 7](https://tex.z-dn.net/?f=n%20%3D%207)
You are told there is a 70% chance of success.
This means that ![p = 0.7](https://tex.z-dn.net/?f=p%20%3D%200.7)
Find the probability the surgery is successful for exactly five patients.
This is P(X = 5).
![P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}](https://tex.z-dn.net/?f=P%28X%20%3D%20x%29%20%3D%20C_%7Bn%2Cx%7D.p%5E%7Bx%7D.%281-p%29%5E%7Bn-x%7D)
![P(X = 5) = C_{7,5}.(0.7)^{5}.(0.3)^{2} = 0.3177](https://tex.z-dn.net/?f=P%28X%20%3D%205%29%20%3D%20C_%7B7%2C5%7D.%280.7%29%5E%7B5%7D.%280.3%29%5E%7B2%7D%20%3D%200.3177)
31.77% probability the surgery is successful for exactly five patients.
4 and 59 hundredths so the 9 is in the hundredths.
It’s D!!! Hope this helped;)
Answer:
3 1/5
Step-by-step explanation:
Since the 12 pizzas are being cut into 8 slices each, that would be 12×8, which is 96. And if you're distributing those 96 slices evenly to 30 people, each person would get 3.2 slices. The mixed number version for 3.2 is 3 2/10, and if you simplify that, the answer would be 3 1/5 slices.