To work out the probability that two members chosen at random are both female, we first need to determine the number of female members in the tennis club.
The ratio of male to female members is 2 : 3. Since the total number of members is 100, we can set up the following equation:
2x + 3x = 100
Combining like terms:
5x = 100
Now, solve for x:
x = 100 / 5
x = 20
So, there are 20 males and 3x = 3 * 20 = 60 females in the tennis club.
Now, let's calculate the probability of choosing two female members at random.
The probability of choosing the first female member is:
P(first member is female) = Number of female members / Total number of members = 60 / 100 = 0.6
After choosing the first female member, there will be one less female member in the club (since we are not replacing the member). So, the probability of choosing the second female member, given that the first member is female, is:
P(second member is female) = Number of remaining female members / Total number of remaining members = 59 / 99 ≈ 0.596
Now, to find the probability of both events happening (choosing two female members in a row), we multiply the individual probabilities:
P(both members are female) = P(first member is female) * P(second member is female) ≈ 0.6 * 0.596 ≈ 0.3576
So, the probability that two members chosen at random are both female is approximately 0.3576 or 35.76%.