# Take Home test on Probability

Take Home test on Probability) N@

Use the chart of sums of rolling 2 dice.

234567

345678

456789

5678910

67891011

789101112

Find the probability of the following sums

P (sum of 4)

Psum of 4=336=112P (sum 3) or P (sum of 5)

Psum 3=236and Psum of 5=436Psum 3 or Psum of 5=236+436=636=16P (sum greater than 8)

Psum greater than 8=1036=518P (sum less than 6)

Psum less than 6=1036=518Use the following chart. Suppose you encounter a delegate at random at a convention.

Women Men

Republicans 20 29

Democrats 24 17

Independents 7 3

Find the following probabilities:

You meet a woman

Pwoman=51100You meet an Independent

Pindependent=10100=110You do not meet a Democrat

Pnot a democrat=1-Pdemocrat=1-41100=59100You meet a female Republican

Pfemale republican=20100=15You meet someone who is not a male Democrat

Pnot a male democrat=1-Pmale democrat=1-17100=83100Use the following deck of cards

Spades Black A K Q J 10 9 8 7 6 5 4 3 2

Hearts Red A K Q J 10 9 8 7 6 5 4 3 2

Clubs Black A K Q J 10 9 8 7 6 5 4 3 2

Diamonds Red A K Q J 10 9 8 7 6 5 4 3 2

Find the following probabilities when selecting one card at a time from a deck of 52 playing cards with the following 26 red, 26 black, 4 of a kind, 13 in each suit

P (K)

PK=452=113P (red card)

Pred card=1352=14P (spade)

Pspade=1352=14P (of at least one Queen if you select a card from the deck 5 times)

Pat least one queen=1-Pnon-queen card=1-48C552C5=1-0.6588=0.34P (10 or a spade)

P10 or spade=P10+Pspade-P10 and spade=452+1352-152=413You have a jar of jelly beans.

5 Red 6 blue 5 yellow 8 orange 2 green and 3 purple

Find the following probabilities if you replace the jelly bean before making another selection

Total number of beans = 5+6+5+8+2+3=29P (green and red)

Pgreen and red=Pgreen×Pred=229529=10841P (blue and blue)

Pblue and blue=629629=36841P (purple and orange and yellow)

Ppurple and orange and yellow=329829529=12024389P (white)

Pwhite=029=0Find the following probabilities if you eat each selected jelly bean before making another selection.

P (yellow and orange and blue

Pyellow and orange and blue=529828627=201827P (red and red and red)

Pred and red and red=529428327=51827 P (black)

Pblack=0Flip a coin three times

These are all the possibilities

H H H

H H T

H T H

H T T

T H H

T H T

T T H

T T T

Find the following probabilities

P (3 tails)

P3 tails=18P (3 heads)

P3 heads=18P (exactly 2 Heads)

Pexactly 2 heads=38P (at least 2 Heads)

Pat least 2 heads=48=12P (more than 1 Tail)

Pmore than 1 tail=1-Pno tail+P1 tail=1-18+38=1-48=12P (4 tails)

P4 tails=0How many telephone numbers can be created if all numbers can be repeated and there are no restrictions.

_ _ __ _ __ _ _ _

If we see the phone number as having three “slots,” one for the area code, one for the first digit, and the third for the remaining six digits, there are 1 way to fill the first slot, 9 ways to fill the second slot, and 10*10*10*10*10*10 = 1000000 ways to fill the last slot, for a total of 1*9*106 = 954 possibilities.

How many 8 letter passwords can be created from the following? 26 Uppercase and 26 lower case letters

Numbers: 0 – 9 Symbols: % $ # * &

All numbers, letters and symbols can be repeated and there are no restrictions

_ _ _ _ _ _ _ _

Only lowercase: 268Only uppercase: 268Only digits: 108Only special: 338Grand total: 95^8−69^8−69^8−85^8−62^8+43^8+59^8+36^8+59^8+36^8+52^8−26^8−26^8−10^8−33^8 = 3025989069143040≈3.026×101

How many outfits can you create from 8 pairs of foot ware, 12 shirts, 9 pairs of slacks, 5 pairs of shorts?

8*12*9*5=4320 outfitsHow many ways can 9 people line up for a bus?

9x8x7x6x5x4x3x2x1, or 362,880 ways of arranging the peopleHow many passwords of 6 digits can be made using the following symbols?

@,#,$,%,&,* Numbers from 0 – 9

All upper and lower case letters

266*266*106*66=4.45*1027 passwordsA restaurant offers 5 vegetables, 6 main dishes, 10 desserts, 8 beverages, and 3 appetizers. How many different meals can be formed?

5*6*10*8*3=7200 meals

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