Probability and Scrabble

[dtweah]

You play in a scrabble tourney. Your probability of winning a game is 0.3 against half of the players, 0.4 against a quarter of the players, and 0.5 against the remaining quarter of the players. You play against a randomly chosen oponent. What is your probability of winning?

A. 0.175

B. 0.195

C. 0.275

D. 0.3

E. 0.375

[dumb.doofus]

I think its E i.e. 0.375

let's say we have 100 people..

so probability of selecting someone from 1st half = 0.5
and so probability of selecting someone from 1st half and then winning = (0.5)*(0.3) ---- (1)

probability of selecting someone from 2nd half = 0.25
and so probability of selecting someone from 2nd half and then winning = (0.25)*(0.4) ---- (2)

probability of selecting someone from 3rd half = 0.25
and so probability of selecting someone from 3rd half and then winning = (0.25)*(0.5) ---- (3)

So total probability of selecting anyone from any category and still winning = (1) + (2) + (3)
= 0.375

[Jose Ferreira]

Additionally, since Group 1, at a probability of 30%, is your most formidable set of challengers, your chances of beating a randomly selected opponent will certainly be higher than 30%. I am a bit surprised by the answer choices, given how quickly someone could have used this reasoning and selected answer (E), simply because it is the only answer with a probability higher than 0.3.

Good guessing strategies can be very helpful, even when you're not pressed for time!