# counting and probability The executives in a company are four women...

counting and probability

The executives in a company are four women and three men. Three are to be chosen at

random to attend a management seminar.

a.

If one of the executives is chosen at random to draw the names out of a hat, what is

the probability that the person drawing the names is a woman?

b.

How many ways can the group of attendees be formed if there are no restrictions on

composition?

c.

How many ways can one man be chosen?

d.

How many ways can 2 women be chosen?

e.

What is the probability that the random selection of the three-person group will

result in two women and one man?

solved

Image transcriptions

Solution
men = It
women = 3
Total = 7
(a) Probability that the person
drawing names is a woman
IS 3 / +
( 6) ways in which attendees can
be formed are If no restrictions
on gender is given by:
= 35 ways
( C) ways in which one mon can
be chosen = ( # ) = 1 ways
(d ) ways in which a women can be
Chosen =
( 2 ) = 3 ways
( @) Probability of 2 women = 2(2)
RF = 6 /7
Probability of one man = /y
= y Probability of i man and a women
= GX H = 24