Question

By rewriting the formula for the multiplication​ rule, you can write a formula for finding

conditional probabilities. The conditional probability of event B​ occurring, given that event A has​ occurred, is

Upper P left parenthesis Upper B vertical line Upper A right parenthesis equals StartFraction Upper P left parenthesis Upper A and Upper B right parenthesis Over Upper P left parenthesis Upper A right parenthesis EndFractionP(B A)=P(A and B)P(A).

Use the information below to find the probability that a flight departed on time given that it arrives on time.

The probability that an airplane flight departs on time is

0.91.

The probability that a flight arrives on time is

0.86.

The probability that a flight departs and arrives on time is

0.84.

Answer 1

Concepts and reason

The probability is defined as the measure of the likelihood that an event will occur. The probability value is always lies between 0 and 1.

Probability distribution assigns a probability value to each of the possible value of a random variable.

Fundamentals

The conditional probability of A given that B is,

From the information, observe that the probability of an airplane flight departs on time is 0.91

The probability that a flight arrives on time is 0.86

The probability that a flight departs and arrives on time is 0.84

Consider A and B are two events that represents the flight departs and arrives on time.

It is symbolically expressed as follows:

The calculation of the required probability is,

Ans:

The calculated probability value is 0.98