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Certainly! Let's break down the problem:
1. The Evil Queen has a basket of 16 apples, and 6 of them are poisoned.
2. Snow White chooses 3 apples at random from the basket.
To find the probability that Snow White awakens after a long time, we need to determine the probability that all three apples she chose are not poisoned.
Let's calculate this probability step by step:
1. Probability of choosing a non-poisoned apple on the first pick: \( \frac{10}{16} \) (since there are 10 non-poisoned apples left out of 16).
2. Probability of choosing a non-poisoned apple on the second pick: \( \frac{9}{15} \) (as there are now 9 non-poisoned apples left out of 15).
3. Probability of choosing a non-poisoned apple on the third pick: \( \frac{8}{14} \) (8 non-poisoned apples left out of 14).
Now, multiply these probabilities together to find the overall probability:
\[ \frac{10}{16} \times \frac{9}{15} \times \frac{8}{14} \]
You can simplify this expression to get the final probability. This represents the chance that Snow White picks three non-poisoned apples in a row.
1. The Evil Queen has a basket of 16 apples, and 6 of them are poisoned.
2. Snow White chooses 3 apples at random from the basket.
To find the probability that Snow White awakens after a long time, we need to determine the probability that all three apples she chose are not poisoned.
Let's calculate this probability step by step:
1. Probability of choosing a non-poisoned apple on the first pick: \( \frac{10}{16} \) (since there are 10 non-poisoned apples left out of 16).
2. Probability of choosing a non-poisoned apple on the second pick: \( \frac{9}{15} \) (as there are now 9 non-poisoned apples left out of 15).
3. Probability of choosing a non-poisoned apple on the third pick: \( \frac{8}{14} \) (8 non-poisoned apples left out of 14).
Now, multiply these probabilities together to find the overall probability:
\[ \frac{10}{16} \times \frac{9}{15} \times \frac{8}{14} \]
You can simplify this expression to get the final probability. This represents the chance that Snow White picks three non-poisoned apples in a row.
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