A box contains 5 blue jellies, some red jelly and rest yellow jelly. The probability of picking a red jelly at random is $\frac{3}{10}$, while the probability of Yellow picking a yellow jelly at random is $\frac{1}{5}$. Find the total number of jellies in the box.

The correct option is 10.

To find the total number of jellies in the box, we can use the probability of picking each type of jelly. Since the box only contains blue, red, and yellow jellies, the sum of their individual probabilities must equal 1.

We are given the following probabilities:

The probability of picking a red jelly: $P\left(\text{Red}\right)=\frac{3}{10}$

The probability of picking a yellow jelly: $P\left(\text{Yellow}\right)=\frac{1}{5}$

First, we can express the probability of picking a yellow jelly with a denominator of 10 to make it easier to calculate:
$P\left(\text{Yellow}\right)=\frac{1}{5}=\frac{2}{10}$

Next, we find the probability of picking a blue jelly by subtracting the probabilities of the red and yellow jellies from 1:

$P\left(\text{Blue}\right)=1-P\left(\text{Red}\right)-P\left(\text{Yellow}\right)$

$P\left(\text{Blue}\right)=1-\frac{3}{10}-\frac{2}{10}$

$P\left(\text{Blue}\right)=1-\frac{5}{10}$

$P\left(\text{Blue}\right)=\frac{5}{10}=\frac{1}{2}$

The probability of picking a blue jelly is also defined as the number of blue jellies divided by the total number of jellies:

$P\left(\text{Blue}\right)=\frac{\text{Number of Blue Jellies}}{\text{Total Number of Jellies}}$

We are given that there are 5 blue jellies in the box. Let $N$ represent the total number of jellies. We set up the following equation:

$\frac{1}{2}=\frac{5}{N}$

Solving for $N$ by cross-multiplying:

$N=5\times 2=10$

Thus, the total number of jellies in the box is 10.