Answer:
[tex]\dfrac{9}{25}[/tex]
Step-by-step explanation:
Given that the bag contains black and red marbles.
Number of black marbles in the bag = 2
Number of red marbles in the bag = 3
Total number of marbles in the bag = Number of black marbles + Number of red marbles = 2 + 3 = 5
Let us have a look at the formula for probability of an event E, which can be observed as:
[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}[/tex]
[tex]P(\text{First red marble}) = \dfrac{\text{Number of red marbles}}{\text{Total number of marbles}} = \dfrac{3}{5 }[/tex]
Now, the marble chosen at first is replaced.
Therefore, the count remains the same.
[tex]P(\text{Second red marble}) = \dfrac{\text{Number of red marbles}}{\text{Total number of marbles}} = \dfrac{3}{5}[/tex]
Now, the required probability can be found as:
[tex]P(\text{First red marble})\times P(\text{Second red marble}) = \dfrac{3}{5}\times \dfrac{3}{5} = \bold{\dfrac{9}{25} }[/tex]
