Question

7).

a.
Let the sample space be S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. Suppose the outcomes are equally likely. Compute the probability of the event E="an odd number less than 7." P(E)= (Type an integer or a decimal. Do not round.)
b.

Answer 1

a)

Given

Sample space , S = {1,2,3,4,5,6,7,8,9,10}

Total number of elements in the sample space = 10

Define E = " an odd number less than 7"

Odd number less than 7 = {1,3,5}

Number of odd number less than 7 = 3

Now

P(E) = 3 / 10 = 0.3

b)

	Died from Cancer	Did not die from Cancer	Total
Never smoked cigars	676	121252	121928
Former cigar smoker	65	8726	8791
Current cigar smoker	131	8775	8906
Total	872	138753	139625

a.

Total number of men = 139625

Number of individuals Died from Cancer = 872

P( died from cancer) = 872 / 139625 = 0.006245 $\approx 0.006$

The probability that he died from cancer = 0.006

b.

Number of individuals current cigar smoker = 131 + 8775 = 8906

P(current cigar smoker ) = 8906 / 139625 = 0.063785  $\approx 0.064$

The probability that he was a current cigar smoker = 0.064

c.

Number of individuals that died from cancer and was a current cigar smoker = 131

P( died from cancer and current cigar smoker ) = 131 / 139625 = 0.000938 $\approx 0.001$

The probability that he died from cancer and was a current cigar smoker = 0.001

d.

From above calculation;

P(died from cancer) = 0.006

P(current cigar smoker ) = 0.064

P(died from cancer and current cigar smoker )= 0.001

Now,

P( died from cancer or current cigar smoker )

= P(died from cancer) + P(current cigar smoker ) - P(died from cancer and current cigar smoker )

= 0.006 + 0.064 - 0.001

= 0.069

The probability that he died from cancer or was a current cigar smoker = 0.069