There are 3 boxes on stage that appear identical, but one is Lucky. The boxes are full of tickets; some are labeled "win" and the others are labeled "lose." In the Lucky box, ninety percent of the tickets are winners. In each of the other two boxes, only twelve percent of the tickets are winners. 1. You will pick a box at random and draw one ticket from it at random.2. What is the probability you will draw a winning ticket? 3. If you do draw a winning ticket, what is the chance it came from the Lucky box?

2.-P = 0.38

3.-P [ Lb | Wt ]  =  0.788

Step-by-step explanation:

1.-Probability of choosing any box is, 1/3. So the probability of choosing the lucky box is 1/3

Let´s say the lucky box is the number 2 box  ( that consideration does not in any way change the problem generality)

Then we have

p₁ probability of choosing box  1 is 1/3   p₁´ Probability of win ticket is  0.12

p₂ probability of choosing box 2 is 1/3  p₂´Probability of win ticket is  0.90

p₃ probability of choosing box 3 is 1/3  p₃´ Probability of win ticket is  0.12

Then

P (of choosing a winning ticket is) = p₁*p₁´ + p₂*p₂´ +  p₃*p₃´

P  =  1/3*0.12 + 1/3*0.9 + 1/3*0.12

P  =  0.04 + 0.3 + 0.04

P = 0.38

3.- if I draw a winning ticket what is the probability it came from Lucky box

According to Bayes theorem

P [ Lb | Wt ]  =   P(Lb) * P[ Wt|Lb]/ P(Wt)

P(Lb) = 1/3  =  0.33333

P[Wt|Lb]  = 0.9

P(Wt) = 0.38

Then By substitution

P [ Lb | Wt ]  =  0.333 *  0.9 / 0.38

P [ Lb | Wt ]  =  0.788

the population of other specie of birds will decline or other specie of birds will find some alternate source of food to survive.

explanation:

according to the competitive exclusion principle, which is also known as gause's law, two specie living in the same niche and feeding on the same resource cannot co-exist stably.

as we have well studied the theory of natural selection which states that only those organisms survive which have better tendency to compete for food and adapt to the environmental conditions.

coming towards the question, what wi ll happen when one species outcompetes the other for the small fish , the other specie will not get enough food and will start to die or decline in population. eventually either other specie needs to find another alternative food source for itself or migrate at some other location where there is less competition otherwise it will just not exist anymore at that niche.

hope it !