Peluang • Part 7: Peluang Kejadian Majemuk Saling Bebas & Tidak Saling Bebas (1)

Compound-Event Probabilities

The video explains the difference between independent events and dependent events using draws from a box containing 4 red balls and 6 blue balls.

Drawing With Replacement: Independent Events

A ball is drawn, its color is recorded, and the ball is returned before the next draw. Since the box’s contents stay the same, the first draw does not affect the probabilities for the second draw.

• First ball red, second ball blue:

[ \frac{4}{10}\times\frac{6}{10}=\frac{6}{25} ]

• Both balls red:

[ \frac{4}{10}\times\frac{4}{10}=\frac{4}{25} ]

• Two balls of different colors: This can happen in either the red–blue or blue–red order.

[ \left(\frac{4}{10}\times\frac{6}{10}\right)

+

\left(\frac{6}{10}\times\frac{4}{10}\right) =\frac{12}{25} ]

These events are independent because replacing the first ball leaves 4 red and 6 blue balls for the next draw.

Drawing Without Replacement: Dependent Events

The first ball is not returned, so the box’s contents—and the probabilities for the second draw—change based on the first result.

• First ball red, second ball blue: After a red ball is drawn, 3 red and 6 blue balls remain.

[ \frac{4}{10}\times\frac{6}{9}=\frac{4}{15} ]

• Both balls red: After the first red ball is drawn, only 3 red balls remain.

[ \frac{4}{10}\times\frac{3}{9}=\frac{2}{15} ]

• Two balls of different colors: Add the probabilities of the red–blue and blue–red orders.

[ \left(\frac{4}{10}\times\frac{6}{9}\right)

+

\left(\frac{6}{10}\times\frac{4}{9}\right) =\frac{8}{15} ]

These events are dependent because the outcome of the first draw changes the number and proportion of balls available for the second draw.

General Method

1. Determine whether the first item is replaced before the next draw.
2. For a sequence of outcomes, multiply the probability at each stage.
3. If an event can occur in multiple orders, calculate each order’s probability and add them.
4. When drawing without replacement, update both the number of favorable outcomes and the total number of possible outcomes after the first draw.

Speakers and Sources

• Narrator/instructor — explains the examples and calculations.
• Jendela Sains — the channel identified in the video’s introduction.