Necklace

[MBA.Aspirant]

A necklace is made by stringing 68 beads together in the repeating pattern: red, green, white, blue and yellow. The necklace design begins with a red bead and ends with a white bead. A bead is pulled out of the necklace at random. What's the probability that the bead is red?

[ntamhane]

Number of Red beads in the Necklace - 14
Number of Green beads in the Necklace - 14
Number of Whit beads in the Necklace - 14
Number of Blue beads in the Necklace - 13
Number of Yellow beads in the Necklace - 13

No. of ways to select 1 bead from 68 = 68
No. of ways to select 1 bead from 14 read = 14
Probability of selecting a read bead = [spoiler]14/68 = 7/34[/spoiler]

[Geva@EconomistGMAT]

Number of Red beads in the Necklace - 14
Number of Green beads in the Necklace - 14
Number of Whit beads in the Necklace - 14
Number of Blue beads in the Necklace - 13
Number of Yellow beads in the Necklace - 13

No. of ways to select 1 bead from 68 = 68
No. of ways to select 1 bead from 14 read = 14
Probability of selecting a read bead = [spoiler]14/68 = 7/34[/spoiler]

This explanation is indeed correct.

@Aspirant, what was your difficulty here?

[Ian Stewart]

I have an issue with the wording of the question. Necklaces are circular; how can you identify where the pattern of beads begins, if there is no 'first bead' in a circular pattern? The question designer ought to have found a different setup in which the pattern is in a line or a row, rather than in a circle. Still, based on what I imagine were the intentions of the question designer, ntamhane's explanation above is perfect.