Question

Find the probability of the indicated event if P(E) = 0.20 and P(F) = 0.45.

Find P(E or F) if P(E and F) = 0.10

P(E or F) = ? (Simplify your answer)

Answer 1

Concepts and reason

The concept of probability is used to solve this question.

Probability is defined as a measure of the likelihood that an event will occur. The probability lies between 0 and 1, where 0 implies the impossibility of the occurrence of the event and 1 implies that the event will certainly occur where the outcomes of the random experiment are considered events.

Fundamentals

Consider two events E and F. The events E and F occur with probabilities $P\left( E \right)$ and $P\left( F \right)$ , respectively.

The probability that either E or F occurs is calculated as:

$P\left( {E \cup F} \right) = P\left( E \right) + P\left( F \right) - P\left( {E \cap F} \right)$

According to the provided information, E and F are the two events, $E \cap F$ denotes that both of the events occur simultaneously, and $E \cup F$ denotes that either of the events E or F occurs.

The probabilities of events are as follows:

$\begin{array}{l}\\P\left( E \right) = 0.20\\\\P\left( F \right) = 0.45\\\\P\left( {E \cap F} \right) = 0.10\\\end{array}$

The probability that either event E or event F occurs is calculated as:

$\begin{array}{c}\\P\left( {E \cup F} \right) = P\left( E \right) + P\left( F \right) - P\left( {E \cap F} \right)\\\\ = 0.20 + 0.45 - 0.10\\\\ = 0.55\\\end{array}$

Ans:

The value of probability is 0.55.

Answer 2

Find P(E or F) if P(E and F) =0.10

Answer 3

Find P(E and F) if P(E or F) = 0.40

Answer 4

Find the probability of the indicated event if

P(E)=0.20

and

P(F)=0.40.

Find P(E or F) if P(E and

F)=0.15