let's firstly convert the mixed fractions to improper fractions and then divide.
![\bf \stackrel{mixed}{1\frac{1}{4}}\implies \cfrac{1\cdot 4+1}{4}\implies \stackrel{improper}{\cfrac{5}{4}}~\hfill \stackrel{mixed}{3\frac{4}{5}}\implies \cfrac{3\cdot 5+4}{5}\implies \stackrel{improper}{\cfrac{19}{5}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{5}{4}\div\cfrac{19}{5}\implies \cfrac{5}{4}\cdot \cfrac{5}{19}\implies \cfrac{25}{76}](https://tex.z-dn.net/?f=%5Cbf%20%5Cstackrel%7Bmixed%7D%7B1%5Cfrac%7B1%7D%7B4%7D%7D%5Cimplies%20%5Ccfrac%7B1%5Ccdot%204%2B1%7D%7B4%7D%5Cimplies%20%5Cstackrel%7Bimproper%7D%7B%5Ccfrac%7B5%7D%7B4%7D%7D~%5Chfill%20%5Cstackrel%7Bmixed%7D%7B3%5Cfrac%7B4%7D%7B5%7D%7D%5Cimplies%20%5Ccfrac%7B3%5Ccdot%205%2B4%7D%7B5%7D%5Cimplies%20%5Cstackrel%7Bimproper%7D%7B%5Ccfrac%7B19%7D%7B5%7D%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20%5Ccfrac%7B5%7D%7B4%7D%5Cdiv%5Ccfrac%7B19%7D%7B5%7D%5Cimplies%20%5Ccfrac%7B5%7D%7B4%7D%5Ccdot%20%5Ccfrac%7B5%7D%7B19%7D%5Cimplies%20%5Ccfrac%7B25%7D%7B76%7D)
Answer:
Step-by-step explanation:
There are 20 ballots, 8 have drawn a car the rest are white.
Find the probability to extract at least one ballot with the drawing of a car if not replaced:
1. If a ballot is taken out:
8 have drawn a car: thus we have 8/20 = 2/5
2. If two ballots are removed, probability of extracting 1 ballot with drawing of car is 8/20 leaving 7 out of 19 remaining. The 7/19 is the probability of drawing out a second ballot with the drawing of a car. Thus we have
8/20 * 7/19 = 56/380 = 14/95
3. If three ballots are removed, probability of extracting 1 ballot with drawing of car is 8/20 leaving 7 out of 19 remaining. The 7/19 is the probability of drawing out a second ballot with the drawing of a car leaving 6 out of 18 remaining. The 6/18 is the probability of drawing out a third ballot with the drawing of a car.
8/20 * 7/19 * 6/18 = 42/855
Answer:
Step-by-step explanation:
