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 = ![P(R)=\dfrac{\text{Number of red marbles}}{\text{Total marbles}}](https://tex.z-dn.net/?f=P%28R%29%3D%5Cdfrac%7B%5Ctext%7BNumber%20of%20red%20marbles%7D%7D%7B%5Ctext%7BTotal%20marbles%7D%7D)
![\\\\=\dfrac{7}{18}](https://tex.z-dn.net/?f=%5C%5C%5C%5C%3D%5Cdfrac%7B7%7D%7B18%7D)
Probability of getting second marble as yellow = ![P(Y)=\dfrac{\text{Number of yellow marbles}}{\text{Total marbles}}](https://tex.z-dn.net/?f=P%28Y%29%3D%5Cdfrac%7B%5Ctext%7BNumber%20of%20yellow%20marbles%7D%7D%7B%5Ctext%7BTotal%20marbles%7D%7D)
![\\\\=\dfrac{2}{18}](https://tex.z-dn.net/?f=%5C%5C%5C%5C%3D%5Cdfrac%7B2%7D%7B18%7D)
Now, the probability that Jon selects a red marble and then a yellow marble :
[ ∵ 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%.