If you can, please give me the detailed explanations with formulas because I am newbie at Stat. Thank you so much!

Question 1

You toss a coin twice. Give:

(i) The probability that you get one head and one tail overall.

(ii) The probability that you get a head on the first throw and a tail on the second.

Question 2

Three fair coins are thrown (and throw are independent of each other).

(i) Find the probability that exactly two are tails.

(ii) You are told that at least one was a tail. What is the probability that they were all tails?

Question 3

Two fair dice are thrown. What is the probability of at least one odd number? What is the probability of this if four fair dice are thrown?

Question 4

In a manufacturing plant, machine A produces 10% of a certain product and machine B produces 90% of this product. Of the production by machine A, 10% are defective, for machine B the defective rate is 5%.

1. (i) If a product is selected at random from one of the machines, what is the probability
2. that it is defective?
3. (ii) If a company inspector sampling production at random discovers a defective product,
4. what is the chance that it came from machine B?

Question 5

Two fair dice are thrown and you are told that the sum of the upturned faces is at least 7. What is the probability that neither of the upturned faces is a 4?