Answer: 6167/6188
This reduces to 881/884
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Step-by-step explanation:
There are 10 good lemons and 7 bad lemons. That's 10+7 = 17 total.
- 7/17 = probability of getting a bad lemon as 1st selection.
- 6/16 = probability of getting a bad lemon as 2nd selection.
- 5/15 = probability of getting a bad lemon as 3rd selection.
- 4/14 = probability of getting a bad lemon as 4th selection.
- 3/13 = probability of getting a bad lemon as 5th selection.
Notice the numerators count down (7,6,5,4,3) and so do the denominators (17,16,15,14,13). This is because each lemon selected is not put back, aka no replacement.
Multiply out those fractions
(7/17)*(6/16)*(5/15)*(4/14)*(3/13)
(7*6*5*4*3)/(17*16*15*14*13)
2520/742560
3/884
The probability of getting 5 bad lemons in a row is exactly 3/884
Subtract that from 1 to determine the probability of getting at least one good lemon. This works because:
P(5 bad lemons) + P(at least one good lemon) = 1
P(at least one good lemon) = 1 - P(5 bad lemons)
So,
P(at least one good lemon) = 1 - P(5 bad lemons)
P(at least one good lemon) = 1 - (3/884)
P(at least one good lemon) = (884/884) - (3/884)
P(at least one good lemon) = (884-3)/884
P(at least one good lemon) = 881/884
That's the fraction when we reduce fully.
But we can multiply top and bottom by 7 to make the denominator 6188
881*7 = 6167
884*7 = 6188
This means that 881/884 = 6167/6188
I'm not sure why your teacher has made the denominator 6188.