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10 mice have taken vaccine. The vaccine has 30% possibility of toxic effects that a mouse may die after taking the vaccine. Question:

What is the possibility that all mice die?

So is the answer to be $0.3^{10}$ or 30% ?

I know the answer that one mouse dies is $0.7^{10}$ but I am not sure how to answer this question.

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The probability of independent events is the product of their probabilities, so the answer is

$$\underbrace{.3 \times .3 \times \cdots \times .3}_\text {10} = 0.3^{10} \approx 0.000006 = 0.0006\, \%.$$

(The probability that all mice die.)

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  • $\begingroup$ I checked again, actually the question at the time when I gave this answer was "how many mice die on average out of total amount of mice" That's was a different question and my answer was wrong. But anyway, now we get it clear:) $\endgroup$
    – almo
    Oct 17, 2020 at 13:19

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