**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) \(= \frac{5}{15} = \frac{1}{3}\)

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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) \(= \frac{5}{15} = \frac{1}{3}\)