Question

Suppose that events E and F are independent, P(E)=0.7, and P(F)=0.8. What is the P(E and F)?

The probability P(E and F) is ______

Answer 1

Concepts and reason

Probability: The ratio of the number of favorable outcomes to certain event and total number of possible outcomes is called as the probability of an event.

Independent events: Let A and B be two events. The events A and B are said to be independent if happening of one event does not affect the happening of another event.

Fundamentals

The probability of an event is defined as,

${\rm{Probability}} = \frac{{{\rm{Number}}\,{\rm{of}}\,{\rm{favorable}}\,{\rm{outcomes}}\,{\rm{for}}\,{\rm{an}}\,{\rm{event}}}}{{{\rm{Total}}\,{\rm{number}}\,{\rm{of}}\,{\rm{outcomes}}}}$

The multiplication rule for independent events, A, and B is,

$P\left( {A \cap B} \right) = P\left( A \right)P\left( B \right)$

The objective of the problem is obtained below:

From the information, the probability of event E is 0.7 and the probability of event F is 0.8 and the events E and F are independent events. The probability of E and F is obtained by using the probability of E and probability of F.

The probability that E and F is obtained below:

The required probability is,

$\begin{array}{c}\\P\left( {E{\rm{ and }}F} \right) = P\left( E \right) \times P\left( F \right)\\\\ = 0.7 \times 0.8\\\\ = 0.56\\\end{array}$

Ans:

Thus, the probability of the event E and F is 0.56.