To solve this problem we use the conditional probability formula:
[tex]P(A|B)=\frac{P(A\cap B)}{P(B)}[/tex]Where P(A|B) is the probability of a given B.
P(A∩B) is the probability of A and B.
ANd P(B) is the probability of B.
In this case, we are asked for the probability that a randomly selected snake is 1 foot long given that the snake is bright orange. Thus:
[tex]\begin{gathered} A\longrightarrow\text{Snake being 1 foot long} \\ B\longrightarrow Snake\text{ is bright orange} \end{gathered}[/tex]We find from the table the probability of A an B, P(A∩B), which is the probability of selecting a snake that is 1 foot long and bright orange:
[tex]P=\frac{Number\text{ of favorable cases}}{Total\text{ number of cases}}[/tex]For the snake to be 1 ft long and bright orange, the number of favorable cases:
And the total number of cases we find by adding all of the numbers from the table:
[tex]4+4+1+3+2+3=17[/tex]Thus:
[tex]P(A\cap B)=\frac{1}{17}[/tex]And the probability P(B) is the probability that the snake is bright orange. For this, the number of favorable cases is:
And the total number of cases is the same, 17.
Thus P(B) is:
[tex]P(B)=\frac{4}{17}[/tex]Now that we have this, we can calculate the conditional probability:
[tex]P(A|B)=\frac{P(A\cap B)}{P(B)}[/tex]Substituting the known probabilities:
[tex]P(A|B)=\frac{\frac{1}{17}}{\frac{4}{17}}=\frac{1}{4}[/tex]The probability is 1/4.
Answer: 1/4
