257/5000 In an envelope 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: 1 If a ballot is taken out. 2 If two ballots are removed. 3 If three ballots are removed.

Question

Britney Alexander

Mathematics

6 August, 05:42

257/5000 In an envelope 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: 1 If a ballot is taken out. 2 If two ballots are removed. 3 If three ballots are removed.

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Georgia Fowler · Answer 1

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