{"id":37418,"date":"2017-05-30T07:24:45","date_gmt":"2017-05-30T14:24:45","guid":{"rendered":"https:\/\/gmatclub.com\/blog\/2017\/05\/land-your-score-probability-problems-primer\/"},"modified":"2023-02-22T07:28:12","modified_gmt":"2023-02-22T14:28:12","slug":"land-your-score-probability-problems-primer","status":"publish","type":"post","link":"https:\/\/gmatclub.com\/blog\/land-your-score-probability-problems-primer\/","title":{"rendered":"A Primer on Probability Problems"},"content":{"rendered":"

GMAT probability problems<\/span><\/h2>\n

Probability is a stated as a percent less than 100 or a fraction less than 1; it is found by dividing the number of <\/span>desired<\/b> outcomes<\/b> by the number of <\/span>possible outcomes<\/b>. So if you are tossing a coin, there are <\/span>two<\/span><\/i> possible outcomes. If you want heads, there is only <\/span>one <\/span><\/i>way to get heads (the coin lands heads up). So the probability is 1 (desired) over 2 (possible), which is 1\/2, or 50%.<\/span><\/p>\n

Multiple events<\/span><\/h2>\n

When multiple events occur, such as multiple coin tosses, each event adds to the total possible outcomes. For the coin example, each toss has 2 possible outcomes. So the denominator for one toss is 2, for two tosses is 4 (2 x 2), for three tosses is 8 (2 x 2 x 2), etc. <\/span>To quickly calculate total possible outcomes, raise the number possible for one event to the power of the number of events<\/b>. For example, the total possible outcomes for 4 coin tosses is <\/span>2<\/span>4<\/span>= 16 possible outcomes.<\/span><\/p>\n

If you want to know the probability of two things happening, you <\/span>multiply<\/b> the probabilities of the two events. So the probability of a coin landing heads up two times is 1\/2 times 1\/2, which is 1\/4. Note that <\/span>the probability of two outcomes both occurring is less than the probability of either outcome occurring alone<\/b>. That\u2019s one way to remember that you multiply to find the probability of multiple items happening; every time you multiply a fraction by a fraction, the value decreases.<\/span><\/p>\n

Non-occurrences<\/span><\/h2>\n

Probabilities are always 100% or less (1.0 or less, if using decimals). If the probability of x occurring is 70%, the probability of x <\/span>not occurring<\/span><\/i> is 100% minus 70%, or 30%. Sometimes on the GMAT, calculating the probability of a desired outcome is complicated. These probability problems are usually solved much more quickly by calculating the <\/span>likelihood of NOT getting the desired outcome, then subtracting that probability from 1<\/b>. Here\u2019s an example:<\/span><\/p>\n

A fair coin is tossed 4 times. What is the probability of getting heads at least twice?<\/span><\/i><\/p>\n

Begin approaching this probability problem by calculating the denominator, the total possible outcomes. As noted above, each toss of the coin yields 2 possible outcomes, so 2 x 2 x 2 x 2 = 16 total possible outcomes.<\/span><\/p>\n

Computing outcomes<\/span><\/h2>\n

The four outcomes could be any combination of H (heads) and T (tails): HTHT, THTH, HHTT, TTHH, HHTH, TTHT, etc. Counting all possible ways to get two or more heads (the number of desired outcomes) would take too long on Test Day, and inexperienced test-takers will waste time doing that. Kaplan-trained test-takers, however, will recognize that the number of UNDESIRED outcomes is much easier to compute: Either no heads at all (TTTT), or heads only once (HTTT, THTT, TTHT, TTTH). That means there are 5 undesired outcomes and a probability of 5\/16 for not getting the desired results.<\/span><\/p>\n

To calculate the probability of heads at least twice, subtract the probability of NOT getting heads at least twice (5\/16) from 100% (16\/16). The probability of getting heads at least twice is 11\/16.<\/span><\/p>\n

You\u2019ll be pretty well set for Test Day if you remember what probability is (desired\/total), how to calculate multiple probabilities (multiply them), and the shortcut for solving difficult probability problems (subtract undesired from 1). <\/span><\/p>\n

Get even more GMAT practice by challenging yourself to a <\/span><\/i>free practice question<\/span><\/i><\/a> every day.<\/span><\/i><\/p>\n

The post Land Your Score: Probability Problems Primer<\/a> appeared first on Business School Insider<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"

GMAT probability problems Probability is a stated as a percent less than 100 or a fraction less than 1; it is found by dividing the number of desired outcomes by…<\/p>\n","protected":false},"author":120,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[9,558,243,940],"tags":[],"class_list":["post-37418","post","type-post","status-publish","format-standard","hentry","category-gmat","category-kaplan-blog","category-blog","category-gmat-prep-gmat","entry"],"aioseo_notices":[],"aioseo_head":"\n\t\t\n\t\n\t\n\t\n\t\n\t\n\n\t\t\n