HSPT Math Question of the Day

1. $\dfrac{1}{2}$
2. $\dfrac{5}{12}$ (correct answer)
3. $\dfrac{1}{3}$
4. $\dfrac{3}{4}$

Explanation: When you encounter probability questions involving "or" situations, you're looking at the probability of multiple favorable outcomes occurring. The key is identifying all the ways you can achieve success, then finding what fraction of total outcomes those represent. To find the probability of landing on blue or yellow, you need to count all the favorable sections. The wheel has 3 blue sections and 2 yellow sections, giving you 3 + 2 = 5 favorable outcomes out of 12 total sections. Therefore, the probability is $\dfrac{5}{12}$, which is answer choice B. Let's examine why the other answers are incorrect. Choice A ($\dfrac{1}{2}$) would require 6 favorable sections out of 12, but blue and yellow only account for 5 sections total. Choice C ($\dfrac{1}{3}$) equals $\dfrac{4}{12}$, which would be correct if you only counted one of the colors (close to the 3 blue sections) but ignored the other. Choice D ($\dfrac{3}{4}$) equals $\dfrac{9}{12}$, which is far too high—this might result from incorrectly adding red and green sections instead of blue and yellow. Remember that "or" in probability means addition when the events can't happen simultaneously. You can't land on both blue and yellow in a single spin, so you simply add the number of blue sections to the number of yellow sections. Always double-check that your numerator reflects all favorable outcomes and your denominator represents the total possible outcomes.