Question

In the United States, there are 59 different species of mammals that are endangered,

75 different species of birds that are endangered, and 68 species of fish that are
endangered. If one animal is selected at random, find the probability that it is either a
mammal or a fish.

Answer 1

To solve this probability problem, we'll follow these steps:

1. Determine the total number of endangered animals across all categories given.
2. Calculate the total number of endangered mammals and fish.
3. Divide the number of endangered mammals and fish by the total number of endangered animals to find the desired probability.

Here's how we do it:

Step 1: Total number of endangered animals
We have 59 mammals, 75 birds, and 68 fish that are endangered. To find the total, we add these numbers together:

Total endangered animals = Number of endangered mammals + Number of endangered birds + Number of endangered fish
Total endangered animals = 59 + 75 + 68

Calculating this gives us:

Total endangered animals = 202

Step 2: Total number of endangered mammals and fish
Now, we combine the number of mammals and fish since we want the probability of selecting either a mammal or a fish:

Endangered mammals and fish = Number of endangered mammals + Number of endangered fish
Endangered mammals and fish = 59 + 68

Calculating this gives us:

Endangered mammals and fish = 127

Step 3: Calculate the probability
The probability that a randomly selected endangered animal is either a mammal or a fish is the number of endangered mammals and fish divided by the total number of endangered animals:

Probability(mammal or fish) = Endangered mammals and fish / Total endangered animals
Probability(mammal or fish) = 127 / 202

This fraction can be simplified if it reduces, but given as it is, it's the exact probability. To give this probability as a decimal or a percentage, you would divide 127 by 202:

Probability(mammal or fish) ≈ 0.6287 (rounded to four decimal places)

To convert this to a percentage, you would multiply by 100:

Probability(mammal or fish) ≈ 62.87%

So, the probability that a randomly selected endangered animal is either a mammal or a fish is approximately 62.87%.

Answer 2

Given Information:

Number of endangered mammal species = 59

Number of endangered bird species = 75

Number of endangered fish species = 68

Required Information:

Probability of either a mammal or a fish = ?

Answer:

P(mammal or fish) = 127/202 = 0.6287 = 62.87%

Explanation:

We want to randomly select one animal and find out the probability of either a mammal or a fish.

The total number of endangered species of animals is given by

Total animals = mammal species + bird species + fish species

Total animals = 59 + 75 + 68 = 202

The probability of selecting a endangered mammal is

P(mammal) = no. of endangered mammal/total no. of endangered animals

P(mammal) = 59/202

The probability of selecting a endangered fish is

P(fish) = no. of endangered fish/total no. of endangered animals

P(fish) = 68/202

Finally, the probability of selecting either a mammal or a fish is

P(mammal or fish) = 59/202 + 68/202

P(mammal or fish) = 127/202

P(mammal or fish) = 0.6287

P(mammal or fish) = 62.87%