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# Given distribution of color beads: blue, black, yellow, white and brown with frequencies $$1, 2, 3, 4,$$...

### Question

Given distribution of color beads: blue, black, yellow, white and brown with frequencies $$1, 2, 3, 4,$$ and $$5$$ respectively. Find the probability that a bead picked at random will be blue or white.

### Options

A) $$\frac{7}{15}$$

B) $$\frac{2}{5}$$

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

D) $$\frac{1}{15}$$

### Explanation:

Total number of beads $$= 15.$$
Number of white beads $$= 4. \Rightarrow \mathrm{P}$$(white) $$= \frac{4}{15}.$$
Number of blue beads $$= 1. \Rightarrow \mathrm{P}$$(blue) $$= \frac{1}{15}.$$
$$\mathrm{P}$$(white or blue) $$= \mathrm{P}$$(white) $$+ \mathrm{P}$$(blue) $$= \frac{5}{15} = \frac{1}{3}$$

## Dicussion (1)

• Total number of beads $$= 15.$$
Number of white beads $$= 4. \Rightarrow \mathrm{P}$$(white) $$= \frac{4}{15}.$$
Number of blue beads $$= 1. \Rightarrow \mathrm{P}$$(blue) $$= \frac{1}{15}.$$
$$\mathrm{P}$$(white or blue) $$= \mathrm{P}$$(white) $$+ \mathrm{P}$$(blue) $$= \frac{5}{15} = \frac{1}{3}$$