**STAT 302 Introduction to Probability Question and Answer**

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**Assessment Details:- **

**Course Code: STAT 302****Course Title: Introduction to Probability****Referencing Styles: Open****Words****: 9000+****University: University of British Columbia****Country: CA**

**Assessment Task:-**

Your solutions will be submitted via Crowdmark. Further instructions will be provided in class. Note that for most of these questions, the final answer is worth little or nothing without a proper solution. Beneath, we expect most solutions to be typed.

- In a game run by a store, and each customer is given a card with 16 squares. The customer is allowed to scratch exactly three squares to reveal whether a square is marked “winner” or “sorry”. Three squares with “winner” on them win a prize. Suppose seven squares are marked “winner” and nine are marked “sorry”. What is the probability a customer will win a prize?

- Two cards are selected without replacement from a usual deck of 52 cards.

(a)How are many points (simple events) in the sample space?

(b)Find the following probabilities:

- both cards are clubs;
- both cards are kings;
- one of the cards is the king of clubs;
- at least one of the cards is a king or a club;
- exactly one of the cards is a face card (J, Q or K).

(c)What is the probability that the second card selected has a lower rank than the first card selected? [Consider an ace as the highest rank only.]

(d)If neither of the two cards selected was spades, what is the probability both were diamonds?

- If P(A) = 0.40, P(B) = 0.50, and P(A1BN) = 0.30,find:

- P(A1B)
- P(B*A)
- P(BN*AN)
- P[(ANcB)N]
- P(AN1BN*AcBN)
- P(AN*B)
- Give the algebraic notation for “the probability that both A and B occur, given that at least one of them occurs”. What is this probability?

- An urn contains 4 balls numbered 0 through 3. One ball is selected at random from the urn and not replaced. All balls with nonzero numbers less than that of the selected ball are also removed from the urn. Then a second ball is selected at random from the remaining in the urn. What is the probability that the second ball selected is numbered 3? As part of your solution, including a probability tree for this experiment.

- Two fair dice are thrown, and the top faces of each die are recorded in order (white, red). Consider the following events: E1: The sum is either 2 or 12.