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- StudyBlue
- Utah
- Utah Valley University
- Mathematics
- Mathematics 2040
- Richard Bennett
- Exam 3 Flash Cards

Will B.

[5.2] What is the probability of drawing a king out of a standard deck?

Is it joint or disjoint?

p(draw king) = 4(kings)/52 = **1/13**

**Disjoint**

[5.2] What is the probability of drawing a queen or a king out of a standard deck?

Is it joint or disjoint?

4(queens)/52 + 4(kings)/52 = 8/52 = **2/13**

**Disjoint**

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[5.2] What is the probability of drawing a 2, 3, or spade out of a standard deck?

Is it joint or disjoint?

4(twos)/52 + 4(threes)/52 + 13(spades) - 2(two of spades and three of spades)/52 = **19/52**

**Not Disjoint**

If 52% of Americans play the lottery, how many don't play?

1-P(Americans that play the lottery) = 1 - 0.52 = **0.48**

[5.3] The probability of 24-year-old males surviving 5 years is 98.86%. **What is the probability 3 males survive?**

(0.9886)(0.9886)(0.9886) = (0.9886)^3 = **0.9958**

[5.3] The probability of 24-year-old males surviving 5 years is 98.86%. **What is the probability 20 males survive?**

(0.9986)^20 = **0.9723**

[5.4] In 2005, 12.64% of all births were preterm. In the same year, 0.22% of all births were overweight. **What is the probability that a birth is preterm and overweight?**

0.0022/0.1264 = 0.0174 = **1.74%**

Conditional Probability Rule

[5.4] The probability that a speeding driver is pulled over is 80%. The probability a ticket is given to who is pulled over is 90%. **What is the probability the speeder gets pulled over and a ticket?**

0.8 * (0.9) = 0.72 = **72%**

General Multiplication Rule

[5.4] Of 100 circuits shipped, 5 are defects. The receiving manager tests 2. If both work, they accept the shipment. **What is the probability they pick at least 1 bad circuit?**

Sample space = GG, GB, BG BB

**GB = 95/100 * 5/99 = 0.048****BG = 5/100 * 95/99 = 0.048****BB = 5/100 * 4/99 = 0.002**

**P(GB) + P(BG) + P(BB) = 0.098**

**1 - P(GG) = 1 - P(0.902) = 0.098**

GG = 95/100 * 94/99 = 0.902

OR

[5.4] A survey of 10,000 African Americans found 27 to have sickle cell anemia. **What is the probability an African American has sickle cell anemia?**

27/10000 = **0.0027**

[5.4] A survey of 10,000 African Americans found 27 to have sickle cell anemia. **What is the probability two African Americans have sickle cell anemia without replacing (Dependent)?**

27/10000 * 26/10000 = **0.00000702**

[5.4] A survey of 10,000 African Americans found 27 to have sickle cell anemia. **What is the probability two African Americans have sickle cell anemia with replacing (Independant)?**

27/10000 * 27/10000 = **0.00000729**

[5.5] A restaurant offers 2 appetizers, 4 entrees, and 2 desserts. **How many combinations are possible?**

2 * 4 * 2 = **16 combinations**

Multiplication Rule

[5.5] 3 letter codes need to be made for an airport. ** How many codes are possible for use with repetition? Without?**

With repetition:

26 * 26 * 26 = **17576**

Without repetition:

26 * 25 * 24 = **15600**

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[5.5] You need to travel to 7 schools. **How many possible routes are there?**

7! = 7 * 6 * 5 * 4 * 3 * 2 * 1 = **5040**

Use __permutation__ since there's no repetition and order matters.

10P3 = 10!/(10-3)! = 10!/7! = (10*9*8*7!)/7! = 10*9*8 = 720

10P3 = 10!/(10-3)! = 10!/7! = (10*9*8*7!)/7! = 10*9*8 = 720

[5.5] How many simple random samples with a size of 4 can be obtained from a class of size 20?

Use __combination__ since there's no repetition and order doesn't matter.

20C4 = 20!/4!(20-4)! = 20!/4!(16!) = 20*19*18*17***16!**/4!*16! = 20*19*18*17/4! = **4845**

[5.5] How many arrangements of flags are there if there are 5 white flags, 3 blue flags, and 2 red?

P = 10!/2!*5!*3! = **2520**

There are 5 ways to get exactly __1__ bad one. (Order doesn't matter so use combination).

(4C1 * 116C4) / 120C5 = ((4!/3!*1!)*(116!/112!*4!))/(120!/5!*115!) = 28640980/190578024 = 15%

(4C1 * 116C4) / 120C5 = ((4!/3!*1!)*(116!/112!*4!))/(120!/5!*115!) = 28640980/190578024 = 15%

[6.1] You ask a basketball player to shoot 3 free throws.

__# of shots made__ __P(x)__

0 0.01

1 0.1

2 0.38

3 0.51

What is the mean? Standard Deviation?

0 0.01

1 0.1

2 0.38

3 0.51

What is the mean? Standard Deviation?

Mean = (0*0.01)+(1*0.1)+(2*0.38)+(3*0.51) = 2.39

Std Dev =

Square Root[ (((0^2 * 0.01) + (1^2 * 0.1) + (2^2 * 0.38) +(3^2 * 0.51)) - (mean^2)) ] = 0.70562029

Std Dev =

Square Root[ (((0^2 * 0.01) + (1^2 * 0.1) + (2^2 * 0.38) +(3^2 * 0.51)) - (mean^2)) ] = 0.70562029

[6.2] Red Cross says 7% of people have O- Blood. They take a sample of 4 people and count the number that have O- blood type. Display sample space, probability for each, and the cumulative distribution function.

P(X=0) P(FFFF)

P(0.93^4) = 0.74805

P(X=1) P(SFFF or FSFF or FFSF or FFFS)

P(4*(0.07*0.93*0.93*0.93)) = 0.22522

P(X=2) P(SSFF or SFSF or SFFS or FSSF or FSFS or FFSS)

P(6*(0.07*0.07*0.93*0.93)) = 0.02543

P(X=3) P(SSSF or SSFS or SFSS or FSSS)

P(4*(0.07*0.07*0.07*0.93)) = 0.00128

P(X=4) P(SSSS)

P(0.07^4) = 0.00002

Cumulative

0.74805201

0.74805201 + 0.22521996 = 0.9733

0.9733 + 0.0254 = 0.9987

0.9987 + 0.0013 = 0.9999

0.9999 + 0.0001 = 1

Binomial Distribution Formula

(nCx)(p^x)(q^(n-x))

(20C15)(0.86^15)(0.14^(20-15)) = (15504)(0.1041062)(0.00005378) = 0.086808 or 8.7%

(nCx)(p^x)(q^(n-x))

(20C15)(0.86^15)(0.14^(20-15)) = (15504)(0.1041062)(0.00005378) = 0.086808 or 8.7%

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