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Please help me on this quick excercise of Probability + A deck is drawn, what is

ID: 2948206 • Letter: P

Question

Please help me on this quick excercise of Probability

+ A deck is drawn, what is the probability that it is a diamond, a clover or a king?

+ Two dice are thrown, determine the following probabilities:
Find the probability that the sum of the values is a multiple of three.
What is the probability of obtaining a multiple of two greater than four?

+ If you throw three coins what is the probability of getting exactly two faces.

+ Two dice are thrown, what is the probability that the sum of both is a prime number?

+ A deck is drawn, what is the probability that it is a diamond, a clover, a number or a king?

+ A domino is extracted, what is the probability that the sum of all the points is a prime number?

+ In a toolbox there are 4 screwdrivers and 5 chisels, if two are extracted consecutively, what is the probability that they are different?

Explanation / Answer

P(clover or a king) = P(clover) + P(king) - P(clover and king)

= 13/52 + 4/52 - 1/52

= 16/52

= 4/13

P(sum of values is a mutiple of 3 when two dice are thrown) = P(at least one die shows 3 or 6)

= 1 - P(both dice doesnt show 3 or 6)

= 1 - (4/6)2

= 5/9

P(multiple of 2 greater than 4 when 2 dice are thrown) = 1 - P(not a multiple of 2 or mutiple of 2 not greater than 4)

= 1 - P(not a mutiple of 2) - P(multiple of two less than or equal to 4)

= 1 - P(both are odd) - P( (1,2), (2,1), (2,2) )

= 1 - (3/6)2 x 3/36

= 1 - 12/36

= 2/3

P(2 faces on a roll of 3 coins) = 3C2 x (1/2)2 x 1/2

= 3/8