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Marrrta [24]
1 year ago
11

C) Three yam tubers are chosen at random from 15 tubers of which 5 are spoilt. Find the probability that, of the three chosen tu

bers: a) none is spoilt b) all are spoilt c) exactly one is spoilt d) at least one is spoilt.
​
Mathematics
1 answer:
Dmitry_Shevchenko [17]1 year ago
7 0

\displaystyle\\|\Omega|=\binom{15}{3}=\dfrac{15!}{3!12!}=\dfrac{13\cdot14\cdot15}{2\cdot3}=455

a)

\displaystyle\\|A|=\binom{10}{3}=\dfrac{10!}{3!7!}=\dfrac{8\cdot9\cdot10}{2\cdot3}=120\\\\P(A)=\dfrac{120}{455}=\dfrac{24}{91}\approx26.4\%

b)

\displaystyle\\|A|=\binom{5}{3}=\dfrac{5!}{3!2!}=\dfrac{4\cdot5}{2}=10\\\\P(A)=\dfrac{10}{455}=\dfrac{2}{91}\approx2.2\%

c)

\displaystyle\\|A|=\binom{10}{2}\cdot5=\dfrac{10!}{2!8!}\cdot5=\dfrac{9\cdot10}{2}\cdot5=225\\\\P(A)=\dfrac{225}{455}=\dfrac{45}{91}\approx49.5\%

d)

A - at least one is spoilt

A' - none is spoilt

P(A)=1-P(A')

We calculated P(A') in a).

Therefore

P(A)=1-\dfrac{24}{91}=\dfrac{67}{91}\approx73.6\%

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