Question

1. Calculate the probability of being dealt the following poker hand. (Recall that a poker player is dealt 5 cards at random from a standard deck of 52.) Express your answer as a decimal rounded to four decimal places. HINT [See Example 3.]

Two pairs: Two cards with one denomination, two with another, and one with a third. Example: 3, 3, Q, Q, J.

2. Your company is considering offering 400 employees the opportunity to transfer to its new headquarters in Ottawa and, as personnel manager, you decide that it would be fairest if the transfer offers are decided by means of a lottery. Assuming that your company currently employs 300 managers, 400 factory workers, and 600 miscellaneous staff, find the following probabilities, leaving the answers as formulas.

(a) All the managers will be offered the opportunity.

C( _____ , _____ ) / C( ________ , ________ )

(b) You will be offered the opportunity.

C( _____ , _____ ) / C( _______ , ______ )

Answer 1

Possible poker hands

Hand with pattern

Number of choices for x and y

Ways to get 2 X's

Similarly, Ways to get 2 X's is 6

We have 44 choice of occurance for Z

Hands with two pairs

So, Probability of Two pairs is

P(Two pairs) = 0.0475