In a room of 50 people, there are 20 men and 30 women. If you randomly select two people from the room, what is the probability that both are women?
First, let's find the probability of selecting a woman on the first draw:

P(woman) = Number of women / Total number of people
         = 30 / 50
         = 0.6

After selecting one woman, there are now 29 women and 49 people remaining in the room. The probability of selecting a woman on the second draw is:

P(woman) = Number of women / Total number of people
         = 29 / 49
         ≈ 0.592

Now, we can find the probability of both events occurring by multiplying the probabilities together:

P(both women) = P(first woman) * P(second woman)
              = 0.6 * 0.592
              ≈ 0.3552

So, the probability of randomly selecting two women from the room is approximately 35.52%.