The Probability of Independent Events

Conditional Probability, Independence, Multiplicative Rules

TOA - Dec 3, 2021

​Conditional Probability

​Conditional Probability is denoted by:

​

​P (B | A)

Multiple Choice

What word is commonly associated with conditional probability?

• and

• given

• or

​Conditional Probability

​The notation is read as "the probability of event B to occur GIVEN that event A occurs" or "the probability of B given A".

​

​Example: The event that your mother will scold you is not certain compared to the event that your mother will scold you given that you were caught playing mobile games during online class hours.

Multiple Select

Which tools are commonly used to help/aid in solving conditional probability problems? [Select ALL correct answers]

​Venn Diagram

​Contingency Table

​If we want to know the probability of a patient who will get defibrillation in less than 2 minutes given that it’s in a medium size hospital, that would be P(<2mins | medium).

​Contingency Table

Independent and Dependent Events

​Two events, A and B, are said to be independent if and only if the probability of event B is NOT influenced or changed by the occurrence of event A, or vice versa. Otherwise, the two events are dependent.

Multiple Choice

Identify whether the events are INDEPENDENT or DEPENDENT:

"Rolling a second die if the outcome of the first die is an odd number".

• Dependent

• Independent

Multiple Choice

Identify whether the events are INDEPENDENT or DEPENDENT:

"Tossing two coins".

• Dependent

• Independent

Multiple Choice

Identify whether the events are INDEPENDENT or DEPENDENT:

"Drawing numbers in the 6/58 Ultra Lotto.".

• Dependent

• Independent

​Multiplicative Rules

​Suppose that we have a fuse box containing 20 fuses, of which 5 are defective. If 2 fuses are selected at random and removed from the box in succession without replacing the first, what is the probability that both fuses are defective?

​Multiplicative Rules

QUIZ​

Get a pen, a paper, and a calculator.​

Multiple Choice

IDENTIFY only which between CONDITIONAL PROBABILITY or MULTIPLICATIVE RULE shall we use to solve the given problem:

One bag contains 4 white balls and 3 black balls, and a second bag contains 3 white balls and 5 black balls. One ball is drawn from the first bag and placed unseen in the second bag. What is the probability that a ball now drawn from the second bag is black?

• Conditional Probability

• Multiplicative Rules

Multiple Choice

Identify which between CONDITIONAL PROBABILITY or MULTIPLICATIVE RULE shall we use to solve the given problem. Solve the problem.

"In a deck of playing cards, what is the probability of getting a Jack given that it is black?"

• Conditional Probability; 0.0769

• Conditional Probability; 0.0192

• Multiplicative Rule; 0.0192

• Multiplicative Rule; 0.0769