The migration pattern of Monarch butterflies are tracked by a catch-and-release method in which individual butterflies are tagged with a circular, lightweight sticker placed carefully on the wings so as not to impede their ability to fly. The sticker contains a unique ID number. Volunteers across the U.S. and South America capture the butterflies, record the IDs if they are tagged, and release them. This allows us to track the locations each unique ID is found, allowing us to estimate the migration pattern. On average, 1 out of 100 captured butterflies are already tagged. Suppose you are a volunteer and capture 50 butterflies; let $X$ denote the number of those that are already tagged. What is the distribution of $X ?$ What is the probability that you catch at least one tagged butterfly?
The migration pattern of Monarch butterflies are tracked by a catch-and-release method in which individual butterflies are tagged with a circular, lightweight sticker placed carefully on the wings so as not to impede their ability to fly. The sticker contains a unique ID number. Volunteers across the U.S. and South America capture the butterflies, record the IDs if they are tagged, and release them. This allows us to track the locations each unique ID is found, allowing us to estimate the migration pattern. On average, 1 out of 100 captured butterflies are already tagged. Suppose you are a volunteer and capture 50 butterflies; let $X$ denote the number of those that are already tagged. What is the distribution of $X ?$ What is the probability that you catch at least one tagged butterfly?
