Question

1)From a deck of 52 cards two cards are drawn Without replacement. What is the probability that both cards are Queens?

2) From set of 12 books how many combinations are there of 12 books taken 4 at a time?

3) A club has 15 members. They must elect a Chairperson, a president, a treasure and a secretary

4) How many different permutations represent the number of possible sets of officers?   

                               

5)   Given the set of random variables and their associated probabilities, This is a Probability       Distribution because the probabilities add up to 1

                  X P(x)

                  0                      1/16

4/16

6/16

4/16

1/16

                          ∑P(x) = 16/16 =1                Find the Mean μ of this probability distribution and standard deviation ð of the distribution.

6)    Using the Binomial Distribution formula find the probability that a family that has 13    children   has 10 girls.

Answer 1

1. There are 4 queens in a deck of 52 cards.

Probability that the first card is a queen = 4/52. After the first queen is drawn, there are now 3 queens in the deck of 51 cards

Probability that the next card is a queen = 3/51

Probability that the first 2 cards are queens = (4/52) x (3/51) = 0.0045

2. Assuming that each book is unique, 4 books can be selected from 12 book set in 12 x 11 x 10 x 9 = 11880 ways.

3. The chairperson can be selected in 15 ways, president in 14 ways, secretary in 13 ways and treasurer in 12 ways.

Total no. of possible combinations = 15 x 14 x 13 x 12 = 32760

4. Part of this question is missing.