Answer:
5/9
Explanation:
If we have a group of 5 men and 4 women, the total number of people we have is 5+4 = 9 people
Total outcome = 9people
For us to select one of each gender without replacement and selecting two at random means we can select a male before a female or a female before a male.
Let W =Women and M = Male
The Probability of selecting two at random without repalcement is given as;
= Pr(W)Pr(M) + Pr(M)Pr(W)
= (4/9*5/8)+(5/9*4/8) (Note that the total number reduces by 1 during the second pick since we aren't replacing the person we picked first)
= 20/72 + 20/72
= 40/72
= 20/36
= 5/9
Hence the the probability that one of each gender is selected is 5/9