Question

a bag contains 5 red, 6 white and 7 black balls. Two balls are drawn at random. What is the probability that both balls are red or both balls are black?

Answer 1

It appears that the two balls are drawn without replacement.
The probability of drawing a red ball first is 5/18. If a red ball has been drawn first, the probability of drawing another red ball on the second draw is 4/17. Therefore the probability of drawing two red balls without replacement is given by:
\[\large P(2\ red)=\frac{5\times4}{18\times17}\]
Using similar reasoning to the above, the probability of drawing two black balls is given by:
\[\large P(2\ black)=\frac{7\times6}{18\times17}\]
The events '2 red balls' and '2 black balls' are mutually exclusive. Therefore we can write:
\[\large P(2\ red)\ or\ P(2\ black)=P(2\ red)+P(2\ black)=you\ can\ calculate\]