Respuesta :
Answer:
The probability that it was raining on Monday given that Shameel misses his flight is 0.5846.
Step-by-step explanation:
The Bayes' theorem states that the conditional probability of an event E[tex]_{i}[/tex], of the sample space S = {E₁, E₂, E₃,...Eₙ}, given that another event A has already occurred is given by the formula:
[tex]P(E_{i}|A)=\frac{P(A|E_{i})P(E_{i})}{\sum\limits^{n}_{i=1} {P(A|E_{i})P(E_{i})}}[/tex]
Denote the events as follows:
X = it will rain on Monday
Y = Shameel misses his flight.
The information provided is:
[tex]P(X) = 0.19\\P(Y|X)=0.06\\P(Y|X^{c})=0.01[/tex]
Compute the probability that it will not rain on Monday as follows:
[tex]P(X^{c})=1-P(X)\\\\=1-0.19\\\\=0.81[/tex]
Compute the probability that it was raining on Monday given that Shameel misses his flight as follows:
Use the Bayes' theorem:
[tex]P(X|Y)=\frac{P(Y|X)P(X)}{P(Y|X)P(X)+P(Y|X^{c})P(X^{c})}[/tex]
[tex]=\frac{(0.06\times 0.19)}{(0.06\times 0.19)+(0.01\times 0.81)}\\\\=\frac{0.0114}{0.0114+0.0081}\\\\=\frac{0.0114}{0.0195}\\\\=0.58462\\\\\approx 0.5846[/tex]
Thus, the probability that it was raining on Monday given that Shameel misses his flight is 0.5846.
