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Question: had help from a very helpful person last time hoping...

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had help from a very helpful person last time, hoping again I can have help with how to get th answers, not just the answers themselves. Thank you

Question. An experiment consists of rolling a fair 6-sided die and choosing a card from a well-shuffled deck of 52 cards. The deck of cards consists of four suits: spades (s), clubs (c), hearts (h) and diamonds (d). There are 13 cards of each suit. The diamonds and hearts are of read colour and clubs and spades are of black colour.

The set of all possible outcomes of this experiment Ω can be defined as follows:

Ω = {1s,2s,3s,4s,5s,6s,1c,2c,3c,4c,5c,6c,1h,2h,3h,4h,5h,6h,1d,2d,3d,4d,5d,6d},

where for example the outcome ’4s’ means the die shows 4 and the chosen card is a spade. Considered are the following events:

• A is the event that the die shows a multiple of 3 and the chosen card is arbitrary (any of the four suits).

• B is the event that the die shows a number less than 4 and the chosen card is of a red colour.

• C is the event that the die shows an even number and the suit of the chosen card is arbitrary.

• D is the event that the number on the die is arbitrary and the chosen card is a heart.

Now do the following

(a) Determine the probabilities of each possible outcomes of the experiment.

(b) Define events A, B, C and D as subsets of Ω and find the probabilities of each event A, B, C and D.

(c) Using the definition of two independent events, decide if A, B, C, D are pairwise independent? ( Hint: there are 6 different pair combinations for these events. To answer this question, check if the definition of independent events is satisfied for each of the pairs.)

(d) Decide if A , C and D are mutually independent. Justify your answer.

(e) Decide if the A , B , C and D are mutually independent. Justify your answer.

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