Question

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?

Answer & Explanation
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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