please help me answer those question! and please explain how to get those answer

Question

please help me answer those question! and please explain how to get those answer!

You have raffle tickets numbered 1 through 100 (inclusive) in a hat. Let Abe the event that a single ticket drawn at random has a number divisible by 5, and let B

be the event that a single ticket drawn at random has a number divisible by 11. Compute the following probabilities:
a) P(A) =

b) P(B) =

c) P(A and B) =

d) P(A or B) =

e) P(A | B) =

Consider the following probability distribution of a random variable X.

x P(x)

0 0.25

100 0.20

200 0.30

300 0.25

(a) Find P(X 200).

(b) Find P(X = 200 | X is 200 or 300)

(c) Find E(X).

(d) Find SD(X).

3. Suppose that a box contains one fair coin (Heads and Tails are equally likely)and one coin with Heads on each side. Suppose further that someone else selects one of the two coins at random, tosses it three times, and gets the outcome
{Heads, Heads, Heads}.
In this problem, you will answer the following question in several parts: What is the probability that the chosen coin was the fair coin?
a) Before tossing the coin, consider the random phenomenon of selecting one of the two coins with equal likelihood. Let F be the event in which the fair coin is chosen.Explain the meaning of the event Fc and compute P(F) and P(Fc) (notice these are NOTconditional probabilities).

b) Let A be the event in which a Heads results from each of the three tosses.Compute P(A | F) and P(A | Fc) and explain what these conditional probabilities mean in context.

c) Draw a tree diagram representing this scenario. The rst branch should be F
and Fc, and the second should be A and Ac. Be sure to include the correct probabilities at each branch.

d) Using your tree diagram, compute P(F and A) and P(Fc and A).

e) Now answer the main question posed in the introduction to this problem.Begin by interpreting that question as a conditional probability and then compute that probability using the results of part d).

Explanation / Answer

1.

a)

There are 100 numbers. 20 are divisible by 5.

P(A) = 20/100 = 0.20 [ANSWER]

***********

b)

9 numbers are divisible by 11 (11,22,33,44,55,66,77,88,99)

P(B) = 9/100 = 0.09 [ANSWER]

***************

c)

P(A and B) = P(divisible by 5 and 11) = P(divisible by 55)

Only 1 number is such, which is 55.

hence,

P(A and B) = 1/100 = 0.01 [ANSWER]

***************

d)

P(A or B) = P(A) + P(B) - P(A and B) = 0.20 + 0.09 - 0.01 = 0.28 [ANSWER]

****************

e)

P(A|B) = P(A and B)/P(B) = 0.01/0.28 = 0.035714286 [ANSWER]

*******************************************

Hi! Please submit the next part as a separate question. That way we can continue helping you! Please indicate which parts are not yet solved when you submit. Thanks!

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