Question

Three ceramic jars contain some red and some green marbles. The number of read green marbles in Jar 1 is in the ratio 5 : 6 and total number of marbles in it are 55. The number of green marbles in Jar 3 is equal to number of green marbles in Jar 1 and number of red marbles in Jar 2 is 5 less than number of red marbles in Jar 1. If Jar 2 and Jar 3 contains 65 and 45 marbles respectively. Then the sum of difference of probabilities of getting red and green marbles from the three jars is​

Answer 1

Given:

Three ceramic jars contain some red and some green marbles. The number of red and green marbles in Jar 1 is in the ratio 5: 6 and the total number of marbles in it are 55. The number of green marbles in Jar 3 is equal to the number of green marbles in Jar 1 and the number of red marbles in Jar 2 is 5 less than the number of red marbles in Jar 1. If Jar 2 and Jar 3 contains 65 and 45 marbles respectively.

To Find:

Then the sum of the difference of probabilities of getting red and green marbles from the three jars is​

Solution:

The ratio of red and green marbles in jar1 is 5:6 and the total marbles are 55, then the number of red and green marbles will be,

$Red=55*\frac{5}{11} \\=25\\Green=55*\frac{6}{11} \\=30$

Now the number of green marbles in jar3 is equal to the number of green marbles in jar1, and the number of red marbles in the jar is (25-5)=20 and the green marbles in jar2 is (65-20)=45

And the number of red marbles in jar 3 will be (45-30)=15

So we have the following data,

JAR1 red=25 green=30

JAR2 red=20 green=45

JAR3 red=15 green=30

Now calculating the  sum of the difference of probabilities of getting red and green marbles from the three jars is​,

$SUM=JAR1+JAR2+JAR3\\=(\frac{30}{55} -\frac{25}{55} )+(\frac{45}{65} -\frac{20}{65} )+(\frac{30}{45} -\frac{15}{45} )\\=\frac{1}{11}+\frac{5}{13} +\frac{1}{3} \\=\frac{347}{429} \\=0.8088$

Hence, the sum of the difference of probabilities of getting red and green marbles from the three jars is​ 0.8088.