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A bag containing 5 red and 5 blue identical balls. Three balls are selected at random without replacement. Determine the probability of selecting balls alternating in colour.

A. 7/18

B. 5/18

C. 5/36

D. 1/36

**Comments**

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alternating in this context means different. That is, selecting first a red ball, then a blue ball and lastly a red ball again. OR selecting first a blue ball, then a red ball and lastly a blue ball again.

Thus, probability of selecting three balls with alternating colours = probability of selecting a red ball (without replacement) x probability of selecting a blue ball (without replacement) x probability of selecting a red ball (without replacement)

OR

probability of selecting three balls with alternating colours = probability of selecting a blue ball (without replacement) x probability of selecting a red ball (without replacement) x probability of selecting a blue ball (without replacement)

In this case, we will be using the first instance (both would give the same answer since the number of blue and red balls are equal)

first: probability of selecting a red ball (without replacement) = 5/10 = 1/2

second: probability of selecting a blue ball (without replacement) = 5/9

third: probability of selecting a red ball (without replacement) = 4/8 = 1/2

Therefore, probability of selecting three balls with alternating colours = 1/2 x 5/9 x 1/2

= 5/36

**Answer C**

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