Even though tetanus is rare in the United States, it is fatal 70% of the time. If three persons contract tetanus during one year, what

is the probability that none of the three will die.

Assume that fatalities due to tetanus are independent of each other.

If they are independent then the multiplication rule applies.
P(x)*P(y)*P(z)= probability all 3 events happen.
The probability for each is 1 - .7 = .3

To find the probability that none of the three people will die from tetanus, we need to calculate the probability that each individual will survive and then multiply these probabilities together.

Since the probability of dying from tetanus is 70%, the probability of surviving is 100% minus 70%, which is 30% or 0.3.

Using the multiplication rule for independent events, the probability that all three individuals will survive is:

P(survive) × P(survive) × P(survive) = 0.3 × 0.3 × 0.3 = 0.027

Therefore, the probability that none of the three people will die from tetanus is 0.027 or 2.7%.