1. **State the problem:** We have a histogram showing the ages of members in a football supporters club with frequency densities for different age intervals. We know there are 20 members aged between 25 and 30. 2. **Calculate the frequency for each age interval:** Frequency is given by frequency density \( \times \) class width. - For 20 to 30: frequency density = 10, width = 10, so frequency = \(10 \times 10 = 100\). 3. **Find the scale factor to convert frequency density to actual number of members:** We know the number of members aged 25 to 30 is 20, which is part of the 20 to 30 interval. Since the whole 20 to 30 interval frequency is 100, but only 20 members are in 25 to 30, this suggests the total frequency for 20 to 30 is 100 but the problem states 20 members between 25 and 30, so the total frequency for 20 to 30 is 100 but the problem states 20 members between 25 and 30, so the total frequency for 20 to 30 is 20. This means the frequency density scale is off by a factor of \(\frac{20}{100} = 0.2\). 4. **Calculate the actual frequencies for all intervals using this scale factor:** - 0 to 10: frequency density = 2, width = 10, frequency = \(2 \times 10 = 20\), scaled frequency = \(20 \times 0.2 = 4\) - 10 to 20: frequency density = 4, width = 10, frequency = \(4 \times 10 = 40\), scaled frequency = \(40 \times 0.2 = 8\) - 20 to 30: frequency density = 10, width = 10, frequency = \(10 \times 10 = 100\), scaled frequency = \(100 \times 0.2 = 20\) (matches given) - 30 to 50: frequency density = 6, width = 20, frequency = \(6 \times 20 = 120\), scaled frequency = \(120 \times 0.2 = 24\) - 50 to 80: frequency density = 1, width = 30, frequency = \(1 \times 30 = 30\), scaled frequency = \(30 \times 0.2 = 6\) 5. **Calculate total number of members:** $$4 + 8 + 20 + 24 + 6 = 62$$ 6. **Calculate the probability that a randomly chosen member is more than 30 years old:** Number of members older than 30 = members in 30 to 50 + members in 50 to 80 = \(24 + 6 = 30\) Probability = \(\frac{30}{62} = \frac{15}{31} \approx 0.484\) **Final answer:** The probability that a randomly chosen member is more than 30 years old is \(\frac{15}{31}\) or approximately 0.484.