Question

A bag contains k blue beads and 4 red ones, If the probability of randomly picking a blue bead from it is 1/3, find the value of k​

Answer 1

`k = 2`

Explanation:

`\textrm{P(blue \;bead)} = \frac{\textrm{Number of blue beads}}{\textrm{Total number of beads}}\\\\\textrm {Number of blue beads } = k\\\\\textrm{Total number of beads } = k + 4\\\\`

`\textrm{P(blue \;bead)} = (k)/(k+4)\\\\`

`\textrm{We are given this probability as } (1)/(3)\\\\\textrm{So,}\\\\(k)/(k+4) = (1)/(3)\\\\`

Cross-Multiplying this equation we get

`k\cdot 3 = 1 \cdot (k + 4)\\\\\longrightarrow 3k = k + 4\\\\3k - k = 4\\\\2k = 4\\\\k = 2\\\\`