Question

Determine which of the following pairs of events are independent.

A: A bird lands on your head.
B: The bird lays an egg.


A: A mosquito lands on your arm.
B: You get a mosquito bite.


A: A Chicagoan visits New York on vacation.
B: He visits Central Park.


A: A green ball is drawn from a box with five balls and placed next to the box.
B: A red ball is drawn next and placed next to the green one.

Answer 1

Independent events are those where event A is not dependent on event B. With changes is another event, the event does not change.

A: A bird lands on your head.

B: The bird lays an egg.

This is independent event as this does not have any correlation between them.

A: A mosquito lands on your arm.

B: You get a mosquito bite.

This is dependent as it is very much possible that a mosquito bites you when it sits on your arm.

A: A Chicagoan visits New York on vacation.

B: He visits Central Park.

This is also dependent event.

A: A green ball is drawn from a box with five balls and placed next to the box.

B: A red ball is drawn next and placed next to the green one.

Lets suppose both the times, balls are taken from the same box. So, this can also be dependent events. If these are from different boxes, then independent events.

Answer 2

Answer: The answers are

* A: A bird lands on your head.

B: The bird lays an egg.

* A: A green ball is drawn from a box with five balls and placed next to the box.

B: A red ball is drawn next and placed next to the green one.

Step-by-step explanation: The first option is

A: A bird lands on your head.

B: The bird lays an egg.

Since there is no connection between statements A and B, so these are independent events.

The second option is

A: A mosquito lands on your arm.

B: You get a mosquito bite.

Since a mosquito will definitely bite if lands on arm, so these are dependent on each other.

The third option is

A: A Chicagoan visits New York on vacation.

B: He visits Central Park.

Central park is in Chicago, so if a person visits central park, he must visit Chicago. Hence, these are dependent events.

The fourth option is

A: A green ball is drawn from a box with five balls and placed next to the box.

B: A red ball is drawn next and placed next to the green one.

Since these two does not depend on each other, so they are dependent.

Thus, the correct options are

* A: A bird lands on your head.

B: The bird lays an egg.

* A: A green ball is drawn from a box with five balls and placed next to the box.

B: A red ball is drawn next and placed next to the green one.