A bucket contains 40 red balls, 25 black balls, and 35 white balls. Two balls are drawn at random. What is the probability that the two balls are black and red?

Answer:

[tex]Probability = \frac{1}{5}[/tex] or [tex]Probability = 0.2[/tex]

Step-by-step explanation:

Given

[tex]Black = 25[/tex]

[tex]White = 35[/tex]

[tex]Red = 40[/tex]

Required

Determine the probability of selecting Black and Red

First, we need to calculate the number of red and black balls

The probability is calculated as thus:

[tex]Probability = P(Black\ and \ Red) \ or\ P(Red\ and \ Black)[/tex]

Convert to mathematical expressions

[tex]Probability = [P(Black) *P(Red)] + [P(Red) *P(Black)][/tex]

Solve for each probaility;

[tex]P(Black) = \frac{Black}{Total} = \frac{25}{100}[/tex]

[tex]P(Red) = \frac{Red}{Total} = \frac{40}{100}[/tex]

So, we have:

[tex]Probability = [P(Black) *P(Red)] + [P(Red) *P(Black)][/tex][tex]Probability = [\frac{25}{100} *\frac{40}{100}] + [\frac{40}{100} *\frac{25}{100}][/tex]

[tex]Probability = [\frac{1000}{10000}] + [\frac{1000}{10000}][/tex]

[tex]Probability = [\frac{1}{10}] + [\frac{1}{10}][/tex]

[tex]Probability = \frac{1+1}{10}[/tex]

[tex]Probability = \frac{2}{10}[/tex]

[tex]Probability = \frac{1}{5}[/tex]

or

[tex]Probability = 0.2[/tex]

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