Biology College

For a particular species of wolf, 55% are female, 20% hunt in medium-sized packs, and 15% are both female and hunt in medium-sized packs. the proportion of wolves that are female but do not hunt in medium-sized packs is

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Answer 1
*Given
Percent of the wolves which are female - 55%
Percent of the wolves which hunt 
     in medium-sized packs                      - 20%
Percent of the wolves which are both
     female and hunt in medium-sized
     packs                                                  - 15%


*Solution

Assuming that there is a total of one hundred wolves in the species, 

1. Since percent (%) means "per 100" or "for every 100" then, 

a. The number of female wolves is

    (55 female wolves / 100 wolves) * 100 wolves total = 55 female wolves

b. The number of wolves that hunt in medium-sized packs is

    (20 wolves / 100 wolves) * 100 wolves total = 20 wolves

    Note that the 20 wolves is a mixture of male and female wolves. 

c. The number of female wolves that hunt in medium-sized packs is

    (15 female wolves / 100 wolves) * 100 wolves total = 15 female wolves

2. Because there is a total of 55 female wolves in the species, and 15 of these wolves hunt in medium-sized packs, then the number of female wolves that do not hunt in medium-sized packs is, 
 
    55 female wolves total - 15 female wolves hunting  = 40 female wolves not
                                                in medium-sized packs         hunting in medium
                                                                                              sized packs

3. To find the proportion, we can express the answer in terms of percent (%) or in fraction, which is usually how proportions are expressed. 

For every 100 wolves, there are 40 female wolves that do not hunt in medium-sized packs. This can be expressed as a proportion of 
 
                                         40  
                                        100

and simplified by dividing both the numerator and denominator by 10, we get,

                                      40/10  
                                     100/10

                                         4   
                                        10

When this is expressed in percent, we multiply the fraction or proportion by 100% to get, 

                                         4      x    100%     = 40%
                                        10

Thus, the proportion of female wolves that do not hunt in medium sized packs is 4/10 or 0.4. When expressed as percent, this is 40%. 
  
Answer 2

1. Probability of neither female nor hunting in medium-sized packs: 0.40.

2. Probability of female given hunting in medium-sized pack: 0.75.

1. To find the probability of wolves that are neither female nor hunt in medium-sized packs, we can use the principle of complementary probability. We start by finding the probability of wolves that are either female or hunt in medium-sized packs or both, then subtract this probability from 1 to get the probability of wolves that are neither female nor hunt in medium-sized packs.

Probability of wolves that are either female or hunt in medium-sized packs or both:

= Probability of females + Probability of hunting in medium-sized packs - Probability of both

= 55% + 20% - 15%

= 60%

Now, the probability of wolves that are neither female nor hunt in medium-sized packs:

= 1 - Probability of wolves that are either female or hunt in medium-sized packs

= 1 - 0.60

= 0.40

Therefore, the probability of selecting a wolf that is neither female nor hunts in medium-sized packs is 0.40.

2. To find the probability of selecting a wolf that is female, given that it hunts in a medium-sized pack, we use conditional probability. We divide the probability of wolves that are both female and hunt in medium-sized packs by the probability of hunting in medium-sized packs.

Probability of selecting a female wolf given that it hunts in a medium-sized pack:

= Probability of both / Probability of hunting in medium-sized packs

= 15% / 20%

= 0.75

Therefore, the probability of selecting a female wolf given that it hunts in a medium-sized pack is 0.75.

Complete Question :

For a particular species of wolf, 55% are female, 20% hunt in medium-sized packs, and 15% are both female and hunt in medium-sized packs. Answer to 2 decimal places, not as a percent.

1. What is the probability of wolves that are neither female nor hunt in medium-sized packs?

2. What is the probability of selecting a wolf that is female, given that it hunts in a medium-sized pack?

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