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Homework #1 Math 3470

1. Find the sample space of the following

a) A student is

determined. (Hint: ACT test scores in mathematics are integers between 1 and 36, inclusive).

b) A coin is ipped three times, and the sequence of heads and tails is observed.

2. One card is

cards. Assume that the

A = fx : xis a jack, queen, or kingg

B = fx : xis a 9,10 or jack and x is redg

C = fx : xis a heartg

D = fx : xis a diamond, a club, or a spadeg

Find a) P(A),P(B), P(C), and P(D); b) P(A \ B), P(A [ B), P(C [ D), and P(C \ D).

3. If P(A) = 0:6, P(B) = 0:5, and P(A \ B) = 0:3, nd a) P(A [ B); b) P(A0 \ B0); c)P(A \ B0). (hint:

A = (A \ B) [ (A \ B0)).

4. If P(A) = 0:6, P(B) = 0:5, and P(A [ B) = 0:9, nd a) P(A \ B); b) P(A0 [ B0).

5. The ve numbers 1,2,3,4, and 5 are written respectively on ve disks of the same size and placed in a hat.

Two disks are drawn without replacement from the hat, and the numbers written on them are observed.

a) List the 10 possible outcomes for this experiment as un-ordered pairs of numbers.

b) If each of the 10 outcomes has probability of 1/10, nd the probability that the sum of the two numbers

drawn is 1) 3; 2) between 6 and 8 inclusive.

6. There are in total 100 balls in a bag. They are either blue or white and either dull or shinny. Assume that

there are 64 blue balls, 46 dull balls. And there are 24 blue and dull balls in the bag. If all the balls are

equally likely to be selected, nd the probability that a white and shinny

1. Find the sample space of the following

**random**experiments:a) A student is

**selected**at random from a math class, and the student's ACT score in mathematics isdetermined. (Hint: ACT test scores in mathematics are integers between 1 and 36, inclusive).

b) A coin is ipped three times, and the sequence of heads and tails is observed.

2. One card is

**drawn**at random from a standard deck of cards. The sample space S is the collection of the 52cards. Assume that the

**probability**function assigns 1/52 to each of these 52 outcomes. LetA = fx : xis a jack, queen, or kingg

B = fx : xis a 9,10 or jack and x is redg

C = fx : xis a heartg

D = fx : xis a diamond, a club, or a spadeg

Find a) P(A),P(B), P(C), and P(D); b) P(A \ B), P(A [ B), P(C [ D), and P(C \ D).

3. If P(A) = 0:6, P(B) = 0:5, and P(A \ B) = 0:3, nd a) P(A [ B); b) P(A0 \ B0); c)P(A \ B0). (hint:

A = (A \ B) [ (A \ B0)).

4. If P(A) = 0:6, P(B) = 0:5, and P(A [ B) = 0:9, nd a) P(A \ B); b) P(A0 [ B0).

5. The ve numbers 1,2,3,4, and 5 are written respectively on ve disks of the same size and placed in a hat.

Two disks are drawn without replacement from the hat, and the numbers written on them are observed.

a) List the 10 possible outcomes for this experiment as un-ordered pairs of numbers.

b) If each of the 10 outcomes has probability of 1/10, nd the probability that the sum of the two numbers

drawn is 1) 3; 2) between 6 and 8 inclusive.

6. There are in total 100 balls in a bag. They are either blue or white and either dull or shinny. Assume that

there are 64 blue balls, 46 dull balls. And there are 24 blue and dull balls in the bag. If all the balls are

equally likely to be selected, nd the probability that a white and shinny

**ball**will be selected.