Question

My local theatre company is going to stage cat on a streetcar named iguana. After the first round of auditions, it is determined that 30% of the applicants can act, 60% look like Marlon Brando, and 52% can simultaneously tap dance while singing. There are 10% of the applicants who possess all three of these attributes and an additional 10% who possess none of these qualities. The casting director says that she’ll be happy with someone who possesses at least 2 of these traits. If 100 people audition, how many satisfactory choices will the casting director have?

Answer 1

The casting director will have 22 satisfactory choices for the roles, based on the criteria of applicants having at least two of the specified traits and given the percentages provided.

Step-by-step explanation:

The casting director's requirement is for someone who possesses at least two of the following traits: acting, looking like Marlon Brando, or the ability to tap dance while singing.

Given that there are 100 people auditioning, according to the provided statistics, 30% can act, 60% look like Marlon Brando, and 52% can tap dance while singing. There are 10% who possess all three attributes and an additional 10% who possess none.

To calculate how many people possess at least two traits, we start by adding the percentages of applicants with each trait (30% + 60% + 52% = 142%) and then subtract both the percentage that have all three traits (10%) and the percentage that possess none (10%). This gives us 142% - 10% - 10% = 122%.

Because percentages greater than 100% indicate overlap, we subtract 100% to correct for this, resulting in 22%. Thus, 22% of the applicants possess at least two of the three traits. Since there are 100 applicants, 22% of 100 is 22 applicants who satisfy the casting director's criteria.