Question

State which events are independent and which are dependent. a. Tossing a coin and drawing a card from a deck b. Drawing a ball from an urn, not replacing it, and then drawing a second ball c. Getting a raise in salary and purchasing a new car d. Driving on ice and having an accident.

Answer 1

Events a and b are independent, event c is dependent, event d is dependent.

Step-by-step explanation:

a. Tossing a coin and drawing a card from a deck

These events are independent because the outcome of tossing a coin does not affect the chance of drawing a card from a deck, and vice versa.

b. Drawing a ball from an urn, not replacing it, and then drawing a second ball

These events are dependent because the outcome of the first draw affects the probability of the second draw, as the ball is not replaced.

c. Getting a raise in salary and purchasing a new car

These events are dependent because the outcome of getting a raise in salary affects the ability to purchase a new car.

d. Driving on ice and having an accident

These events are dependent because driving on ice increases the probability of having an accident.

Answer 2

Independent events do not affect each other's outcomes, while dependent events have outcomes that can be influenced by one another. Tossing a coin and drawing a card are independent. Drawing balls without replacement, getting a raise and buying a car (typically), and driving on ice and having an accident are dependent events.

Step-by-step explanation:

To determine whether events are independent or dependent, we must consider the effect of one event on the probability of another occurring. When discussing the relationship between events, we also encounter concepts like mutually exclusive events and sampling with replacement or without replacement.

Event Analysis:

• a. Tossing a coin and drawing a card from a deck are independent events because the outcome of one does not affect the outcome of the other. This is under the assumption that a coin toss doesn't change what card you draw from the deck, and vice versa.

• b. Drawing a ball from an urn, not replacing it, and then drawing a second ball are dependent events. This is because once the first ball is drawn and not replaced, it changes the composition of the urn for the second draw, affecting the probability of the second event.

• c. Getting a raise in salary and purchasing a new car can be considered dependent events in many practical scenarios because getting a raise might influence one's decision to purchase a new car. However, without context, it could be argued that such life events are independent if one does not affect the probability of the other occurring.

• d. Driving on ice and having an accident are dependent events. The act of driving on ice increases the probability of having an accident due to the slippery conditions.