You have a bowl of 100 grapes, with one of them being poisonous. If you randomly eat 10 grapes, the probability of eating the poisonous grape can be calculated as follows:
1.The total number of ways to choose 10 grapes from 100 is:
\text{Total ways} = \binom{100}{10}
However, we don’t need to compute this directly.
2.The number of ways to choose 10 grapes that do not include the poisonous one is:
\text{Ways to choose 10 from the 99 non-poisonous grapes} = \binom{99}{10}
3.The probability of avoiding the poisonous grape is:
P(\text{avoid}) = \frac{\binom{99}{10}}{\binom{100}{10}}
This simplifies to:
P(\text{avoid}) = \frac{99}{100} \times \frac{98}{99} \times \frac{97}{98} \times \dots \times \frac{90}{91}
Which simplifies further to:
P(\text{avoid}) = \frac{90}{100} = 0.9
4.Therefore, the probability of eating the poisonous grape is:
P(\text{eat poison}) = 1 - P(\text{avoid})
= 1 - 0.9
= 0.1 \text{ or } 10\%
So, the chance of eating the poisonous grape is 10%.
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