Question

A bag contains four white and three black marbles. One marble selected, its color is noted, and then it is returned to the bag. Then a second marble is selected, what is the probability that both selected marbles are white?

Answer 1

Hint:
Probability: The chance of the happening of an event is termed as probability.
Events: An outcome of a random experiment is called an event.

Two events A and b are independent of one another if the occurrence of event A does not affect the probability that event B occurs and vice-versa.
In this case,
The probability that both events A and event B occur P(AB) is the product of P(A) and P(B).
If the events A and B are not independent, they are said dependent.

Complete step by step solution:
Given,
The number of white marbles $ = 4$
The number of black marbles $ = 3$
Total number of marbles $ = 7$
The number of ways of selecting the first ball such that it is white is 4.
Then
   The probability $ = \dfrac{4}{7}$
The number of ways of selecting the second ball such that it is white is 4.
$\therefore $ the probability that both selected marbles were white is $\dfrac{4}{7} \times \dfrac{4}{7} = \dfrac{{16}}{{49}}$
Because both events are independent to each other.

Hence the probability that both selected marbles were white is $\dfrac{{16}}{{49}}$.

Note: If we replace the marbles in the bag each time, then the chances do not change and the events are independent.
With replacement: the events are independent (the chances don’t change)
Without replacement: the events are dependent (the chances change).