Respuesta :
Answer:
The probability is 0.5
Step-by-step explanation:
If the time follows a continuous and uniform distribution, the probability that Alice makes the dinner in less than x minutes is equal to:
[tex]P(X\leq x)=\frac{x-a}{b-a}[/tex]
where a and b are equal to 19 and 45 minutes respectively. So:
[tex]P(X\leq x)=\frac{x-19}{45-19}[/tex]
Now, Let's call A the event that Alice takes more than 40 minutes to finish making dinner and B the event that Alice takes more than 35 minutes to finish making dinner. So, the probability that it takes Alice more than 40 minutes to finish making dinner given that it has already taken her more than 35 minutes in the making of her dinner is equal to:
P(A/B)=P(A∩B)/P(B)
Then, the probability P(B) that Alice takes more than 35 minutes to finish is calculated as:
[tex]P(B)=P(x\geq35)=1-P(x\leq 35)=1-\frac{35-19}{45-19}=0.3846[/tex]
At the same way, the probability P(A∩B) that Alice takes more than 40 minutes to finish making dinner and Alice takes more than 35 minutes to finish making dinner is equal to the probability P(A) that Alice takes more that 40 minutes to finish making dinner, so it is calculated as:
[tex]P(A)=P(x\geq40)=1-P(x\leq 40)=1-\frac{40-19}{45-19}=0.1923[/tex]
Finally, P(A/B) is equal to:
[tex]P(A/B)=\frac{0.1923}{0.3846}=0.5[/tex]
The calculated probability is "0.50".
[tex]\to f(x) = \frac{1}{b-a}= \frac{1}{45-19}=\frac{1}{26}[/tex]
We have to find:
[tex]\to (p < 40 |> 35) = \frac{P(>40 \bigcap > 35 )}{P(> 35)}[/tex]
[tex]=\frac{\int^{45}_{40} f(x) \ dx}{\int^{45}_{35} f(x) \ dx }\\\\=\frac{\frac{45-40}{26}}{\frac{45-35}{26}}\\\\=\frac{\frac{5}{26}}{\frac{10}{26}}\\\\= \frac{5}{26} \times \frac{26}{10}\\\\= \frac{5}{10}\\\\=0.50[/tex]
Since, the probability of Alice would need more than 40 min to finish her supper is 0.50, considering that she has already spent and over 35 minutes preparing her food.
Learn more about time amount:
brainly.com/question/15097275
