Answer the questions below The space will expand as you work

Answer the questions below. The space will expand as you work. Please include your entire working calculations along with your answer. Minimum credit is given if you only include your final answer.

1. Write each as a set and then give the probability, of the following happening?

From a full pack of picture cards (J,Q,K,A) an ace is dealt?

From a set of a single die that a 4 is rolled?

From the birth of quadruplets 2boys and 2 girls are born?

2. Write the total number of possible combinations of 5 dice being rolled at once?

3. Using a standard cell phone keypad, how many random words (just letters strung together) can be produced from the PIN 23579?

1

2

ABC

3

DEF

4

GHI

5

JKL

6

MNO

7

PQRS

8

TUV

9

WXYZ

0

4. With an IP address how many times can the bit pattern 101001 appear?

5. Using arrow diagrams If 7 dice are rolled, and explain why must two at least be the same value?

1	2 ABC	3 DEF
4 GHI	5 JKL	6 MNO
7 PQRS	8 TUV	9 WXYZ
	0

Solution

1.a

By assuming that you are only counting picture cards(cards those have pictures)

In full pack of cards we have total 16(4*4) cards,those have pictures.(4 in each suit),and total 4 aces(1 in each suit).

So P(An ace is dealt from picture cards) = total ace / total cards with pictures

= 4/16 = 1/4

If you are counting entire deck then

P(dealt with ace) = 4 / 52 (total 52 cards and 4 aces)

1.b

In a dice we have total 6 numbers from 1 to 6 (total 6 possiblities), and coming of 4 on rolled dice have only 1 possible way.

So P(4 is rolled) = 1/6

1.c

There are total 16 ways(4*4) and total 4 ways to be 2 girls and 2 boys.

So P = 6/16

2.

Total number of possible combinations of 5 dice being rolled at once = (possible number of combination of 1 dice being rolled) ^ 5

Total number = 6 ^ 5 = 6*6*6*6*6 = 7776

3.

I am assuming that by given PIN means we can press that button to generate the words i.e if PIN is 2 then total 3 words (\'A\' , \'B\', \'C\') can be made and if PIN is 23 then total 9 words can be made( ABC * DEF = \'AD\' , \'AE\' , \'AF\' , \'BD\' , \'BE\' , \'BF\' , \'CD\' , \'CE\' , \'CF\')

So by PIN 23579 total words can be made = (ABC * DEF * JKL * PQRS * WXYZ) = (3 * 3 * 3 * 4 * 4) = 432

4.

In an IP address we have total 32 bits and our bit pattern have 6 bits.

And I am assuming that all the patterns are separate i.e. not overlapping to each other

than this bit pattern (\"101001\") of length 6 can appear max of 5 times.

Ans = 4

5.

On each dice we have total 6 numbers from 1 to 6.So if we roll 7 dices together ,then atleast 2 of them will roll same value.