1

Part of 2023 Assara - South Russian Girl's MO

Problems(2)

percentages in a survey

Source: 2023 South Russian Girls MO - Assara Juniors p1

A survey of participants was conducted at the Olympiad.

50\%

of the participants liked the first round,

60\%

of the participants liked the second round,

70\%

of the participants liked the opening of the Olympiad. It is known that each participant liked either one option or all three. Determine the percentage of participants who rated all three events positively.

percentages in a survey , senior version

Source: 2023 South Russian Girls MO - Assara Seniors p1

A survey of participants was conducted at the Olympiad.

90\%

of the participants liked the first round,

60\%

of the participants liked the second round,

90\%

of the participants liked the opening of the Olympiad. Each participant was known to enjoy at least two of these three events. Determine the percentage of participants who rated all three events positively.