All About Red & Blue Marbles

or Independent and Dependent Probability

Biglie by flickr user mat.teo

A coin is flipped three times. Draw a tree diagram to illustrate the sample space.

A fair six-sided die is rolled twice. Draw a chart to illustrate the sample space.

A fair six-sided die is rolled twice. Draw a chart to illustrate the sample space.

A bus is scheduled to arrive at a train station at any time between 07:05 and 07:15 inclusive. A train is scheduled to arrive between 07:11 and 07:17 inclusive. The arrival of a bus at 7:06 and a train at 07:14 can be represented by the ordered pair (6, 14). Times are expressed in whole minutes.

e) What is the probability of the bus arriving after the train?

d) How many ordered pairs have the train arriving after the bus?

c) How many ordered pairs have the bus and the train arriving at the same time?

b) How many ordered pairs are there in this sample space?

a) Sketch a sample space for this event (use a chart).

A marble is drawn, replaced and a second marble is drawn from a bag containing 3 red and 3 blue marbles. What is the probability that the second marble is blue?

A marble is drawn, replaced and a second marble is drawn from a bag containing 3 red and 3 blue marbles. What is the probability that the second marble is blue?

Dependent and independent probabilities ...

A bag contains 6 marbles, 3 red and 3 blue. A marble is chosen at random and then REPLACED back in the bag. A second marble is selected, what is the probability that it is blue?

Independent EventsEvents in which the outcome of one event does not affect the outcome of the other event.

A marble is drawn, not replaced and a second marble is drawn from a bag containing 3 red and 3 blue marbles. What is the probability that the second marble is blue?

A marble is drawn, not replaced and a second marble is drawn from a bag containing 3 red and 3 blue marbles. What is the probability that the second marble is blue?

A marble is drawn, not replaced and a second marble is drawn from a bag containing 3 red and 3 blue marbles. What is the probability that the second marble is blue?

Dependent and independent probabilities ...A bag contains 6 marbles, 3 red and 3 blue. A marble is chosen at random and NOT REPLACED back in the bag. A second marble is selected, what is the probability that it is blue?

Dependent EventsIf the outcome of one event affects the outcome of another event, then the events are said to be dependent events.

Identify each of the following as experiments involving dependent in independent events.

INDEPENDENT

(a) Toss a coin and roll a die six.

DEPENDENT

Drag and Drop Baby!

(c) Draw 2 cards from a 52 card deck, with replacement.

(b) Draw 2 cards from a 52 card deck, without replacement.

INDEPENDENT

DEPENDENT

INDEPENDENT

In a family of 3 children, with boys and girls equally likely to be born, what is the probability that exactly 2 kids are girls?

Two marbles are drawn. If the 1st marble is blue it is discarded and replaced with a red. Similarly, if the 1st marble is red it is discarded and replaced with a blue one. What is the probability that the second marble is blue?

Two marbles are drawn. If the 1st marble is blue it is discarded and replaced with a red. Similarly, if the 1st marble is red it is discarded and replaced with a blue one. What is the probability that the second marble is blue?