In a certain office, we have 30 female workers and 70 male workers. The probability
of having a smoker worker given that he is a male is 0.6 and the probability of having a
smoker worker given that she is a female is 0.4. Select a person at random from this office.
Find
a. The probability that this person will be a smoker.
b. Given that this person is a smoker, what is the probability that this person will be a male.
c. The probability that this person will be a smoker or a male

Step-by-step explanation:

a)

P(f ) = probability of being female = .3

P(m ) Probability of being male = .7

P(s/m) =  probability  of having a smoker worker given that he is a male = .6

P(s/f) =  probability  of having a smoker worker given that he is a male = .4

p(s) = p(m) x p(s/m) + p(f) x P(s/f)

= .7 x .6 + .4 x .3

= .42 + .12

= .54

b )

p (m/s) =  probability that this person will be a male,Given that this person is a smoker

p(m) x p(s/m) /  [ p(m) x p(s/m) + p(f) x P(s/f) ]

= .7 x .6 / .7 x .6 + .4 x .3

= .42 / .54

= .78

c )

Probability of the person being a smoker and male

= .54 x .78 = .42

probability of a person being a male and non smoker = .7 - .42 = .28

probability of a person being a non smoker and female = .46 -.28 =.18

probability that  person will be a smoker or a male

= 1 - (a person being a non smoker and female).  

= 1 - .18

= .82 .

let x be the money she spent so that she can earn the free t-shirt.

since, she already spent $112.49

⇒

also, as per the statement: jennifer must spend $250 or more in order to qualify for a free t-shirt at the store.

then,

we have an inequality i.,e

subtract 112.49 from both sides we get;

therefore, $137. 51 more money does jennifer need to spend so that she can earn the free t-shirt

b. 1.25 hr

step-by-step explanation:

if you have a constant speed of 60 mph, then you have a ratio between 60 mi. to 1 hr. dividing both sides by 60 we get the ratio

1 mi. to

then mult. both sides by 75 we get the ratio

75 mi. to

simplifying we get

75 mi. to

or 1.25 hr.