Question

Annie brought 10 bagels to school, 7 of which are Asiago cheese.

If Annie randomly gives away 5 bagels to teachers, what is the probability that e
the chosen bagels are Asiago cheese?

Answer 1

The probability that 5 chosen bagels of which exactly 3 are Asiago cheese = 0.3087 or 30.87%

Explanation:

Given:

Total bagels brought to school = 10

Number of Asiago cheese bagels = 7

To find the probability of randomly choosing 5 Asiago cheese bagels of which exactly 3 are Asiago cheese.

Solution:

Let probability of choosing an Asiago cheese bagel be the successful event.

Probability of choosing one Asiago cheese bagels =
`(7)/(10)=0.7`

Probability of success = 0.7

Probability of failure ( not choosing an Asiago cheese bagel) = 1 - Probability of success =
`1-0.7=0.3`

Using Bernoulli Trials

To calculate the binomial probability of obtaining exactly
`r` events in
`n` trials the formula used is:

⇒
`nCr.p^r.q^((n-r))`

where
`p\rightarrow` Probability of success

`q\rightarrow` Probability of failure

Thus, probability of randomly choosing 5 Asiago cheese bagels of which exactly 3 are Asiago cheese can be calculated as :

⇒
`5C3(0.7)^3(0.3)^2`

⇒
`(5!)/((5-3)!3!)(0.343)(0.09)`

⇒
`(5!)/((2)!3!)(0.343)(0.09)`

⇒
`10(0.343)(0.09)`

⇒
`0.3087\ or\ 30.87\%` (Answer)