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%.
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?