Question
The probability of growing a seedling from a seed is 0.62. How many seeds do I need to plant so that the probability of growing at least one seedling is greater than or equal to 0.87?
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Answer to a math question The probability of growing a seedling from a seed is 0.62. How many seeds do I need to plant so that the probability of growing at least one seedling is greater than or equal to 0.87?
Hank
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Let’s assume that the probability of growing a seedling from a seed is p = 0.62. We want to find the number of seeds we need to plant so that the probability of growing at least one seedling is greater than or equal to 0.87.
Let’s call the number of seeds we need to plant n. The probability of not growing a seedling from a single seed is 1 - p = 0.38. Therefore, the probability of not growing a seedling from n seeds is (1 - p)^n. The probability of growing at least one seedling is the complement of the probability of not growing any seedlings, which is 1 - (1 - p)^n.
We want to find the smallest integer value of n such that 1 - (1 - p)^n >= 0.87. Using a calculator, we can solve for n and get n >= 5.
Therefore, we need to plant at least 5 seeds to ensure that the probability of growing at least one seedling is greater than or equal to 0.87.
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