Final answer:
To calculate the probability that exactly 2 out of 3 tomato plants live after transplanting, with a survival rate of 70%, we use the binomial probability formula. The calculation gives us a probability of approximately 0.44 or 44% when rounded to the nearest hundredth.
Step-by-step explanation:
The question asks us to calculate the probability that exactly 2 out of 3 tomato plants will survive after being transplanted, given that the survival rate for each plant is 70%. To find this probability, we can use the binomial probability formula, which is P(X = k) = nCk * p^k * (1-p)^(n-k), where n is the number of trials, k is the number of successes, p is the probability of success on a single trial, and nCk is the number of combinations.
For this problem:
- n = 3 (the number of plants)
- k = 2 (we want exactly 2 plants to live)
- p = 0.7 (the probability of any one plant living)
The number of combinations of n things taken k at a time is given by the binomial coefficient, calculated as nCk. Thus, we have 3C2 = 3.
The probability calculation is:
P(X = 2) = 3C2 * 0.7^2 * (1-0.7)^(3-2) = 3 * 0.49 * 0.3 ≈ 0.441
So, the probability that exactly 2 of the 3 tomato plants will live after transplanting is approximately 0.44 or 44% when rounded to the nearest hundredth.