Question

A certain cancer treatment successfully treats the cancer 70% each time it is administered. My mom survived for 8 months using the treatment. What is the probability that the treatment was successful 8 months in a row? Round your final answer to the nearest tenth of a percent.

Answer 1

5.80%

Explanation:

Given:

The probability of successful treatment of cancer is,
`P(Success)=70\%=0.7`

The probability of successful treatment in a given month is independent of the other month. So, probability of successful treatment for 'n' months in a row is given as:

`P(n-Successes)=(P(Success))^n`

Plug in 8 for 'n' and determine the required probability. This gives,

`P(8-successes)=(0.7)^8=0.0576=5.76\%\approx5.80\%`

Therefore, the probability that the treatment was successful 8 months in a row is 5.80% rounded to nearest tenth of a percent.