Question

5. In a bag 8 red and some blue balls. If one ball selected
randomly, then red ball and blue ball probability ratio is
2:5, then find probability of blue ball ?​

Answer 1

ANSWER:

Given:

• 8 red balls and some blue balls in a bag.
• Probability ratio of picking red ball to blue ball = 2:5

To Find:

• Probability of blue ball

Assumption:

• Let the number of blue balls be x.

Solution:

$:\implies\text{\sf{Total number of balls = Number of red balls + Number of blue balls}}\\\\:\implies\text{\sf{Total number of balls = 8 + x}}\\\\\text{\sf{So,}}\\\\:\implies\text{\sf{Probability of picking a red ball [P(R)] = \sf{\dfrac{8}{8+x}} }}\\\\:\implies\text{\sf{Probability of picking a blue ball [P(B)] = \sf{\dfrac{x}{8+x}} }}\\\\\text{\sf{But we are given that,}}\\\\:\implies\text{\sf{P(R) : P(B) = 2 : 5}}\\\\:\implies\text{\sf{ \sf{\dfrac{8}{8+x}:\dfrac{x}{8+x}} = 2 : 5}}$

$:\implies\sf{\dfrac{\left(\dfrac{8}{8+x}\right)}{\left(\dfrac{x}{8+x}\right)}} = \sf{\dfrac{2}{\:\:5\:\:}}\\\\\text{\sf{So, (8+x) gets cancelled,}}\\\\:\implies\sf{\dfrac{\:\:8\:\:}{x}}=\sf{\dfrac{\:\:2\:\:}{5}}\\\\\text{\sf{On Cross Multiplying,}}\\\\:\implies \sf{40 = 2x} \\\\:\implies \sf{x = 20}\\\\:\implies\text{\sf{Total number of balls = 8 + x = 8 + 20 = 28}}\\\\\bf{:\implies P(B) = \dfrac{x}{8+x} = \dfrac{20}{28} = \dfrac{5}{7}}$

∴ Probability of picking a blue ball is 5/7.

Answer 2

Answer:

Step-by-step explanation: