Respuesta :
Answer:
The probability that 5 chosen bagels of which exactly 3 are Asiago cheese = 0.3087 or 30.87%
Step-by-step 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 = [tex]\frac{7}{10}=0.7[/tex]
Probability of success = 0.7
Probability of failure ( not choosing an Asiago cheese bagel) = 1 - Probability of success = [tex]1-0.7=0.3[/tex]
Using Bernoulli Trials
To calculate the binomial probability of obtaining exactly [tex]r[/tex] events in [tex]n[/tex] trials the formula used is:
⇒ [tex]nCr.p^r.q^{(n-r)}[/tex]
where [tex]p\rightarrow[/tex] Probability of success
[tex]q\rightarrow[/tex] Probability of failure
Thus, probability of randomly choosing 5 Asiago cheese bagels of which exactly 3 are Asiago cheese can be calculated as :
⇒ [tex]5C3(0.7)^3(0.3)^2[/tex]
⇒ [tex]\frac{5!}{(5-3)!3!}(0.343)(0.09)[/tex]
⇒ [tex]\frac{5!}{(2)!3!}(0.343)(0.09)[/tex]
⇒ [tex]10(0.343)(0.09)[/tex]
⇒ [tex]0.3087\ or\ 30.87\%[/tex] (Answer)
