Question

On a camping trip, Kimberly kept a log of the types of snakes she saw. She noted their colors and approximate lengths. 1 foot long 2 feet long Red 4 4 Bright orange 1 3 Bright green 2 3 What is the probability that a randomly selected snake is 1 foot long given that the snake is bright orange? Simplify any fractions

Answer 1

To solve this problem we use the conditional probability formula:

`P(A|B)=(P(A\cap B))/(P(B))`

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:

`\begin{gathered} A\longrightarrow\text{Snake being 1 foot long} \\ B\longrightarrow Snake\text{ is bright orange} \end{gathered}`

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:

`P=\frac{Number\text{ of favorable cases}}{Total\text{ number of cases}}`

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:

`4+4+1+3+2+3=17`

Thus:

`P(A\cap B)=(1)/(17)`

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:

`P(B)=(4)/(17)`

Now that we have this, we can calculate the conditional probability:

`P(A|B)=(P(A\cap B))/(P(B))`

Substituting the known probabilities:

`P(A|B)=((1)/(17))/((4)/(17))=(1)/(4)`

The probability is 1/4.

Answer: 1/4