Answer:
[tex]\sf \dfrac{65}{121}[/tex]
Step-by-step explanation:
Probability is a measure of how likely events are to happen.
When all the possible outcomes are equally likely, we can use this formula to calculate the probability of an event happening:
[tex]\sf P(event)=\dfrac{\textsf{Number of outcomes where event happens}}{\textsf{Total number of possible outcomes}}[/tex]
Given that the bag contains 7 red marbles and 4 blue marbles, the total number of possible outcomes is 11.
Therefore:
[tex]\textsf{Probability of drawing a red marble}=\sf \dfrac{7}{11}[/tex]
[tex]\textsf{Probability of drawing a blue marble}=\sf \dfrac{4}{11}[/tex]
Given that the marble is replaced after it has been chosen, the probability of drawing two of each color are:
[tex]\sf P(Red)\;and\;P(Red)=\dfrac{7}{11} \times \dfrac{7}{11}=\dfrac{49}{121}[/tex]
[tex]\sf P(blue)\;and\;P(blue)=\dfrac{4}{11} \times \dfrac{4}{11}=\dfrac{16}{121}[/tex]
Therefore, the probability of drawing two reds OR two blues is:
[tex]\sf P(Red+Red)\;or\;P(Blue+Blue)=\dfrac{49}{121}+\dfrac{16}{121}=\dfrac{65}{121}[/tex]
