1. MULTI-STEP PROBLEM There are 5743 known
amphibian species in the world. Of these,
1856 species are judged to be at risk of
extinction, and another 113 species may
already be extinct.
a. Find the probability that an
amphibian species chosen at
random is at risk of extinction
or may already be extinct.
b. Find the probability that two
different amphibian species,
each chosen at random, are at
risk of extinction.
To find the probabilities, we need to know the total number of amphibian species.
Given:
Total number of known amphibian species = 5743
Number of amphibian species at risk of extinction = 1856
Number of amphibian species that may already be extinct = 113
a. Probability that an amphibian species chosen at random is at risk of extinction or may already be extinct:
There are two ways an amphibian species can be at risk or extinct:
1. At risk of extinction only
2. May already be extinct
To calculate the probability:
Probability = (Number of species at risk + Number of species that may already be extinct) / Total number of species
Probability = (1856 + 113) / 5743
Probability = 1969 / 5743
b. Probability that two different amphibian species, each chosen at random, are at risk of extinction:
First, we need to calculate the probability of choosing an amphibian species at risk for the first species, and then adjust the probability for the second species.
Probability of choosing a species at risk for the first species = Number of species at risk / Total number of species
Probability of choosing a species at risk for the second species = (Number of species at risk - 1) / (Total number of species - 1)
To calculate the probability:
Probability = (Number of species at risk / Total number of species) * ((Number of species at risk - 1) / (Total number of species - 1))
Probability = (1856 / 5743) * ((1856 - 1) / (5743 - 1))
To find the probabilities in this multi-step problem, we need to calculate the number of favorable outcomes and divide it by the total number of possible outcomes. Let's break it down step by step:
a. The probability that an amphibian species chosen at random is at risk of extinction or may already be extinct:
1. Find the number of amphibian species at risk of extinction or may already be extinct. This is the sum of the two given numbers: 1856 + 113 = 1969.
2. Find the total number of known amphibian species: 5743.
3. Divide the number of species at risk of extinction or may already be extinct by the total number of known species: 1969/5743.
So, the probability is 1969/5743.
b. The probability that two different amphibian species, each chosen at random, are at risk of extinction:
1. The first amphibian species is chosen at random. The probability of it being at risk of extinction is 1856/5743.
2. The second amphibian species is chosen at random, considering that the first one is already chosen. As the question states, you need to find the probability that two DIFFERENT species are both at risk of extinction. So, the number of amphibian species at risk of extinction decreases by one, and the total number of known species also decreases by one: (1856-1)/(5743-1).
3. Multiply the probabilities from step 1 and step 2 to find the combined probability: (1856/5743) * ((1856-1)/(5743-1)).
So, the probability is (1856/5743) * ((1856-1)/(5743-1)).