Question

PLEASE HELP 22 POINTS URGENT

Answer 1

`\binom{18}{0}(0.7)^(18)+\binom{18}{1}(0.3)^1(0.7)^(17)`

This will be a binomial probability, since there are two options - either cured or not cured.

We want the probability that less than or equal to one person is cured. This means we want the probability that either 0 people are cured or 1 person is cured.

To find the probability of 0 people being cured, we take a combination of 18 people chosen 0 at a time:

`\binom{18}{0}`

We multiply this by the probability of someone being cured, 0.3, raised to the number of people being cured, 0:

`\binom{18}{0}(0.3)^0\\\\=\binom{18}{0}(1)=\binom{18}{0}`

Lastly we multiply this by the probability of someone not being cured, 1-0.3, raised to the number of people not being cured, 18:

`\binom{18}{0}(1-0.3)^(18)\\\\=\binom{18}{0}(0.7)^(18)`

To find the probability of 1 person being cured, we take a combination of 18 people chosen 1 at a time:

`\binom{18}{1}`

We multiply this by the probability of someone being cured, 0.3, raised to the number of people being cured, 1:

`\binom{18}{0}(0.3)^1`

Lastly we multiply this by the probability of someone not being cured, 1-0.3, raised to the number of people not being cured, 17:

`\binom{18}{0}(0.3)^1(1-0.3)^(17)\\\\=\binom{18}{0}(0.3)^1(0.7)^(17)`

Answer 2

The probability that "at most 1" will be cured is the probability that 0 or 1 will be cured. The attachment shows how that is calculated.