1. Four cards are dealt off the top of a well-shuffled standard deck of cards. Y

Question

1. Four cards are dealt off the top of a well-shuffled standard deck of cards. You have a choice:

(a) To win $1 if the first card is a club and the second is a diamond and the third is a heart and the fourth is a spade.

(b) To win $1 if the four cards are of four different suits. (Hearts, diamonds etc are called suits.)

Which option is better?

3. Jane has three children, each of which is equally likely to be a boy or a girl independently of the others. Define the events:

B = {there is at most one boy}

C ={the family includes one boy and one girl}

Are B and C independent?

3.If I roll a fair 6 sided die 5 times, the chance that I roll at least 1 even number is...

Explanation / Answer

We are allowed to do 1 question at a time. Post again for second question.

1) Note that the phrase IN THAT ORDER = "AND"; you must get a club AND a diamond AND a heart AND a spade:

Pr (C and D and H and S ) = (13 / 52) * (13 / 51) * (13 / 50) * (13 / 49) = 28,561 / 6,497,400 = 0.0044

The phrase "IN ANY ORDER" = "OR" You must get CDHS OR CDSH OR DCHS OR .... If you list all possibilities, you will find there are 24 of them.

So the chance of winning bet B will be 24 times that of winning bet A -- adding P (CDHS) + P (CDSH) + P (DHCS) ... = 24 * P(CDHS) = 0.1055 or 10.55 percent.

So, B option is better.

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