corrected question:A jar contains two blue and five green marbles. A marble is drawn at random and then replaced. A second marble drawn at random. For each of the following, find the probability that: a) both marbles are blue b) both marbles are the same color c)the marbles are different in color
Answer:
Step-by-step explanation:
<u><em>The probability was done with replacement.</em></u>
Probaility of an event happening![=\frac{number of required outcomes}{number of possible outcomes}](https://tex.z-dn.net/?f=%20%3D%5Cfrac%7Bnumber%20of%20required%20outcomes%7D%7Bnumber%20of%20possible%20outcomes%7D)
number of blue marbles= 2
number of green marbles=5
total number of marbles=7
(a) probability that both marbles are blue = pr(first is blue)*pr(second is blue)
![=\frac{2}{7}*\frac{2}{7}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B2%7D%7B7%7D%2A%5Cfrac%7B2%7D%7B7%7D)
![=\frac{4}{49}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B4%7D%7B49%7D)
(b)probability that both marbles are the same color =pr(first is blue)*pr(second is blue) + Pr(first is green)*Pr(second is green)
![=\frac{4}{49} + \frac{5}{7}*\frac{5}{7}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B4%7D%7B49%7D%20%2B%20%5Cfrac%7B5%7D%7B7%7D%2A%5Cfrac%7B5%7D%7B7%7D)
![=\frac{4}{49} + \frac{25}{49}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B4%7D%7B49%7D%20%2B%20%5Cfrac%7B25%7D%7B49%7D)
![=\frac{29}{49}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B29%7D%7B49%7D)
(c)Probability that the marbles are different in colors=pr(first is blue)*pr(second is green) + Pr(first is green)*Pr(second is blue)
![=\frac{2}{7}*\frac{5}{7}+ \frac{5}{7}*\frac{2}{7}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B2%7D%7B7%7D%2A%5Cfrac%7B5%7D%7B7%7D%2B%20%5Cfrac%7B5%7D%7B7%7D%2A%5Cfrac%7B2%7D%7B7%7D)
![=\frac{10}{49}+\frac{10}{49}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B10%7D%7B49%7D%2B%5Cfrac%7B10%7D%7B49%7D)
![=\frac{20}{49}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B20%7D%7B49%7D)