Answer to Question #268966 in Statistics and Probability for Light

Question

a) A company that plans to hire one new employee has prepared a final list of six candidates, all of whom are equally qualified. Four of these six candidates are women. If the company decides to select at random one person out of these six candidates,

i. What is the probability that this person will be a woman?

ii. What is the probability that this person will be a man?

iii. Do these two probabilities add up to 1.0? If yes, why?

b) A couple is planning their wedding reception. The bride’s parents have given them a choice of four reception facilities, three caterers, five DJs, and two limo services. If the couple randomly selects one reception facility, one caterer, one DJ, and one limo service, how many different outcomes are possible?

Answer 1

a)

i)

$P=4/6=2/3$

ii)

$P=2/6=1/3$

iii)

These two probabilities add up to 1.0 because woman and man are mutually exclusive events, they cannot happen simultaneously.

b)

possible outcomes of reception facilities: 4

possible outcomes of caterers: 3

possible outcomes of DJs: 5

possible outcomes of limo services: 2

total possible outcomes:

$4\cdot3\cdot5\cdot2=120$