Home » » If P = $$\frac{2}{3}$$ ($$\frac{1 - r^2}{n^2}$$), find n when r = $$\frac{1}{3}$$ ...

# If P = $$\frac{2}{3}$$ ($$\frac{1 - r^2}{n^2}$$), find n when r = $$\frac{1}{3}$$ ...

### Question

If P = $$\frac{2}{3}$$ ($$\frac{1 - r^2}{n^2}$$), find n when r = $$\frac{1}{3}$$ and p = 1

### Options

A) $$\frac{3}{2}$$

B) $$\frac{1}{3}$$

C) 3

D) $$\frac{2}{3}$$

### Explanation:

If P = $$\frac{2}{3}$$ ($$\frac{1 - r^2}{n^2}$$), find n when r = $$\frac{1}{3}$$ and p = 1
p = $$\frac{2(1 - r^2)}{3n^2}$$ when r = $$\frac{1}{3}$$ and p = 1
1 = $$\frac{2}{3}$$ $$\frac{(1 - (\frac{1}{3})^2)}{n^2}$$
n2 = $$\frac{2(3 - 1)}{3 \times 3}$$
n2 = $$\frac{2 \times 2}{3 \times 3}$$
= $$\frac{4}{9}$$
n = $$\frac{4}{9}$$
= $$\frac{2}{3}$$

## Dicussion (1)

• If P = $$\frac{2}{3}$$ ($$\frac{1 - r^2}{n^2}$$), find n when r = $$\frac{1}{3}$$ and p = 1
p = $$\frac{2(1 - r^2)}{3n^2}$$ when r = $$\frac{1}{3}$$ and p = 1
1 = $$\frac{2}{3}$$ $$\frac{(1 - (\frac{1}{3})^2)}{n^2}$$
n2 = $$\frac{2(3 - 1)}{3 \times 3}$$
n2 = $$\frac{2 \times 2}{3 \times 3}$$
= $$\frac{4}{9}$$
n = $$\frac{4}{9}$$
= $$\frac{2}{3}$$