Question

1. If a seed is planted, it has a 85% chance of growing into a healthy plant.
f 10 seeds are planted, what is the probability that exactly 4 don't grow?

2.Suppose that 37% of people own dogs. If you pick two people at random, what is the probability that they both own a dog?

3.A CBS News poll conducted June 10 and 11, 2006, among a nationwide random sample of 651 adults, asked those adults about their party affiliation (Democrat, Republican or none) and their opinion of how the US economy was changing ("getting better," "getting worse" or "about the same"). The results are shown in the table below.

	better	same	worse
Republican	38	104	44
Democrat	12	87	137
none	21	90	118

Express your answers as a decimal and round to the nearest 0.001 (in other words, type 0.123, not 12.3% or 0.123456).

If we randomly select one of the adults who participated in this study, compute:

P(Republican) =

P(same) =

P(same|Republican) =

P(Republican|same) =

P(Republican and same) =

4. In a large school, it was found that 73% of students are taking a math class, 80% of student are taking an English class, and 54% of students are taking both.

Find the probability that a randomly selected student is taking a math class or an English class. Write your answer as a decimal, and round to 2 decimal places if necessary.


Find the probability that a randomly selected student is taking neither a math class nor an English class. Write your answer as a decimal, and round to 2 decimal places if necessary.

Answer 1

1) If a seed is planted, it has a 85% chance of growing into a healthy plant.

  N=10 seeds planted

p= 100% - 85% = 15% = 0.15 , we are interested in the plant NOT growing

(1-p) = 85% = 0.85 , 85% chance the plant will survive and grow

k=4, we want four of them to fail

the probability that exactly 4 don't grow is ,

= 0.04

2) Suppose that 37% of people own dogs. Two people at random have pick,

Probability of dog-ownership for one person chosen at random = 0.37

Probability of dog-ownership for two person chosen at random = 0.372 = 0.1369

3)

	better	same	worse	total
Republican	38	104	44	186
Democrat	12	87	137	236
None	21	90	118	229
Total	71	281	299	651

If we randomly select one of the adults who participated in this study,

P(Republican) = 186/651 = 0.286
P(same) = 281/651 = 0.432
P(same|Republican) = P(same and republican) / P(Republican) = (104/651) / (186/651) = 0.559
P(Republican|same) = P(same and republican) / P(same) = (104/651) / (281/651) = 0.370
P(Republican and same) = 104/651 = 0.160

4)   In a large school, it was found that 73% of students are taking a math class, 80% of student are taking an English class, and 54% of students are taking both.

P(math) = 0.73 , P(english) = 0.80 , P( English and math) = 0.54

   the probability that a randomly selected student is taking a math class or an English class.

P( math or english) = P(math) + P(english) - P( English and math)

= 0.73 + 0.80 - 0.54 = 0.99

the probability that a randomly selected student is taking neither a math class nor an English class.

P( math or english)c = 1 - P(math or english) = 1 - 0.99 = 0.01

  

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