If a disease has a 10% chance of transmission per contact, what is the probabili

If a disease has a 10% chance of transmission per contact, what is the probability of not transmitting the disease after 3 contacts? (2022)

If a disease has a 10% chance of transmission per contact, what is the probability of not transmitting the disease after 3 contacts? (2022)

Step 1: Understand that the disease has a 10% chance of being transmitted per contact.
Step 2: Calculate the probability of not transmitting the disease in one contact. This is done by subtracting the transmission chance from 1: 1 - 0.1 = 0.9.
Step 3: Since we want to find the probability of not transmitting the disease after 3 contacts, we need to multiply the probability of not transmitting in one contact by itself three times: 0.9 * 0.9 * 0.9.
Step 4: This can be simplified using exponents: 0.9^3.
Step 5: Calculate 0.9^3, which equals 0.729.

Probability of Independent Events – The question tests the understanding of calculating the probability of independent events occurring multiple times, specifically using the complement rule.
Complement Rule – It assesses the ability to apply the complement rule, where the probability of an event not occurring is calculated as 1 minus the probability of the event occurring.