3. (3 points) Suppose a fair coin is flipped and a fair six-sided die is rolled.

Question

3. (3 points) Suppose a fair coin is flipped and a fair six-sided die is rolled. List the (3 points) One card is selected at random from a deck of 52. What is the probability 5. (8 points) Two fair six-sided dice are rolled. What is the probability that one die shows members of the event "the die lands on an odd number" that the card is an ace or a four? exactly three more than the other die (for example, rolling a 1 and 4, or rolling a 6 and a 3) 6. (6 points) Suppose a student who has not studied (shamel) takes an 5-question true false quiz and guesses at the answer to every question (a) What is the probability that the student answers every question incorrectly? b) What is the probability that the student answers at least one question correctly? (c) What is the probability that the student answers eractly 2 questions correctly?

Explanation / Answer

Question 3

Here if Coin results are Head (H) and Tail (T) and dice rolls are from 1 to 6.

so, the die lands on an odd number has sample space

= (H,1) , (T,1) , (H,3) , (T,3) , (H,5), (T,5)

Question 4

Total ace = 4 and total fours = 4

so total positive possibilities are = 4 + 4 = 8

so, Pr(Ace or 4) = 8/52 = 2/13

Question 5

Here the sample space of the given condition is (1,4), (4,1) , (2,5) , (5,2) , (3,6), (6,3)

so total possibilities = 6

so Pr(That aforesaid event) = 6/36 = 1/6

Question 6

True false quiz

Pr(True) = Pr(False) = 0.5 ; number of question = 5

(a) Here if x is the total correct answer given by the student.

Pr(X = 0) = Pr(x = 0 ; 5 ; 0.5) = 5C0 (0.5)5  = 0.03125

(b) Pr(At least one question correctly) = 1 - Pr(no question correctly)

= Pr(x >= 1) = 1 - Pr(X = 0) = 1 - Pr(x = 0 ; 5; 0.5) = 1 - 0.03125 = 0.96875

(c) Pr(X = 2) = 5C2 (0.5)5 = 0.3125

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