Two cards are drawn without replacement from a standard deck of 52 playing cards

Question

Two cards are drawn without replacement from a standard deck of 52 playing cards. What is the probability of choosing a heart and then a club? 0.0577 0.0637 0.0588 0.06250 Two cards are drawn with replacement from a standard deck of 52 playing cards. What is the probability of choosing a heart and then a club? 0.0588 0.0637 0.0625 0.0577 If a single fair die is rolled, find the probability of a 5 given that the number rolled is odd. 1/2 1 2/3 1/6 1/3 Out of 300 applicants for a job, 100 are female, 200 of the applicants have graduate degrees, and 70 of the applicants are female and have a graduate degree. What is the probability that a randomly chosen applicant is male, given that the applicant has a graduate degree? 0.0588 0.0577 0.650 0.70 The newly elected president needs to decide the remaining 4 spots available in the cabinet he/she is appointing. If there are 10 eligible candidates for these positions (where rank matters), how many different ways can the members of the cabinet be appointed? 0.70 5040 210 0.65 Customer account "numbers" for a certain company consist of 2 letters followed by 3 numbers. How many different account numbers are possible if repetitions of letters and digits are not allowed? 1, 404,000 468,000 1, 757, 600 676,000 How many ways can Rudy choose 4 pizza toppings from a menu of 9 toppings if each topping can only be chosen once? 3, 024 504 126 84 An English teacher needs to pick 4 books to put on his reading list for the next school year. He has narrowed down his choices to 10 novels and 8 plays. How many different ways can he choose the books if he wants to include exactly one play? 126 720 128 960 A contractor is considering a sale that promises a profit of $36,000 with a probability of 0.7 or a loss (due to bad weather, strikes, and such) of $4000 with a probability of 0.3. What is the expected profit? $26, 400 $28,000 $32,000 $24,000 $25, 200

Explanation / Answer

1)

There are 13 hearts and 13 club in 52 cards so required probability is

(13/52)*(12/51) = 0.0588

2)

Since cards are drawn with replaement so requried probability is

(13/52)*(13/52) = 0.0625

3)

When we roll a single die possible outcomes are 1, 2, 3, 4, 5, or 6. Out of these six outcomes, three outcomes are odd. And out of these three odds outcome one outcome is 5. So requried probability is 1/3.

4)

From the given we can find that

Number of males out of 300 is: Male = 300-100=200

Number of males and graduate degrees : 200 -70 = 130

And we have

P(males) = 200/ 300

P(males and graduate degree) = 130/300

So the required probability is

P(graduate degree|males) = P(males and graduate degree) / P(males) = 130 / 200 = 0.65

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