Answer: about 0.0432 or 4.32%
Step-by-step explanation:
Given : A bag of marbles contains 7 red, 5 blue, 4 green, and 2 yellow marbles.
Total marbles = 7+5+4+2=18
Let R : Event of getting first marble as red .
Y= Event of getting second marble as yellow.
Jon selects a marble, replaces it, then selects another marble.
⇒Both events are independent .
Probability of getting first marble as red = [tex]P(R)=\dfrac{\text{Number of red marbles}}{\text{Total marbles}}[/tex]
[tex]\\\\=\dfrac{7}{18}[/tex]
Probability of getting second marble as yellow = [tex]P(Y)=\dfrac{\text{Number of yellow marbles}}{\text{Total marbles}}[/tex]
[tex]\\\\=\dfrac{2}{18}[/tex]
Now, the probability that Jon selects a red marble and then a yellow marble :
[tex]P(R)\times P(Y)=\dfrac{7}{18}\times\dfrac{2}{18}\approx0.0432=4.32\%[/tex] [ ∵ Event R and Y are independent .]
Hence, the probability that Jon selects a red marble and then a yellow marble is about 0.0432 or 4.32%.
