PLEASE HELP! I have questions regarding basic probability for statistics that I

Question

PLEASE HELP! I have questions regarding basic probability for statistics that I do not understand at all :[. Can someone please help me? There are several parts but I am unsure of how to start and believe I am doing it completely wrong. Help would be so very much appreciated! Thanks in advance! Here is the relevant information for the problem:

You perform feeding trials on the coastal horned lizard Phrynosoma coronatum and determine how many ants a lizard eats each day. At the end of the experiment you determine that individuals ate between 1 and 4 ants per day, and the probability was exactly equal for each of these outcomes.

(a) What is the probability of each outcome?

(b) Your advisor, the famous herpetologist, then asks you to determine how probable it is for a lizard to eat 2 or fewer ants. What do you tell her?

(c) A graduate student in the lab wants to know the probability that his first focal lizard will eat 1 ant, the second focal lizard will eat 2 ants, and the third focal lizard will eat 3 ants. Because he didn’t take biometrics, he asks you to calculate the correct answer. What do you tell him (after you tell him to learn basic probability theory)?

(d) Because you are now the superstar in the lab, a fellow undergraduate student in the lab asks you what is the probability that a lizard will eat 4 ants after 2 days. What do you tell her?

(e) You are back in lab talking about lizards again after acing your Genetics exam–because you understand probability theory. Using a Venn Diagram, show your fellow undergraduate the sample space for a foraging lizard after 2 days. 5 On the Venn 5 Hint: think about combining the outcomes after day 1 and the outcomes after day 2, (e.g., one outcome is that the lizard ate 2 ants on the first day and 3 ants on the second day = (2,3)). Diagram, show the following sets: - The set in which the lizard ate 4 ants after two days. - The set of outcomes that your advisor asked you about–two or fewer ants on the first day.

(f) What is the intersection between these two sets? What is the probability of this intersection?

(g) What is the union between these two sets? What is the probability of this union?

(h) What is the conditional probability that a lizard will eat 4 ants after 2 days, given it ate 1 or 2 ants during the first day?

Explanation / Answer

We define Probabilty in the following way

(a) Probbabilty of an event = Points in favour of the event / Total number of points in the sample space.

Here Prob. ( a lizard eats ants ) = Numbers of ants eaten by a lizard /4

and as the probability was exactly equal for each of these outcomes.

Prob.( a lizard eats 1 ant) = 1/4

Prob ( a lizard eats 2 ants ) = 2/4 and so on.

(b) The probability that a lizard to eat 2 or fewer ants would be as folllows:

Let A= the event that a lizard eats 1 ant is A and 2 be B, then it is Prob (A or B)

Here Prob. (A or B ) P(AUB) = P(A) + P(B) - P(A^B) = 1/4 + 2/4 - 1/4 = 2/4

(c) According to the problem, as the condition gien in the probabilty are equally likely

Prob.( the first lizard will eat 1 ant) = 1/4

Prob.( the 2nd will eat 2 ant) = 2/4

Prob( the 3d will eat 3 ants) = 3/4 etc.

(d) Once the number of days are considered, the total number of point will change. If it is two days total points be 8 and the probability that a lizard will eat 4 ants in 2 days will be

P( a lizard will eat 4 ants in two days ) = 4/8 = 1/2

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