Question

If a seed is planted, it has a 70% chance of growing into a healthy plant. If 7 seeds are planted, what is the probability that fewer than 3 grow into a healthy plant?

Answer 1

The probability that fewer than 3 seeds grow into a healthy plant is 0.8781%.

Step-by-step explanation:

To find the probability that fewer than 3 seeds grow into a healthy plant, we need to find the probability that 0, 1, or 2 seeds grow. The probability of a seed growing into a healthy plant is 70%, so the probability of a seed not growing is 100% - 70% = 30%. Using the binomial probability formula, we can calculate the probabilities for each case:

P(0 seeds grow) = (7 choose 0) * (0.3)^0 * (0.7)^7 = 0.000028

P(1 seed grows) = (7 choose 1) * (0.3)^1 * (0.7)^6 = 0.000775

P(2 seeds grow) = (7 choose 2) * (0.3)^2 * (0.7)^5 = 0.007978

Adding up these probabilities gives us the probability of fewer than 3 seeds growing: 0.000028 + 0.000775 + 0.007978 = 0.008781, or 0.8781%