Post Follow-up: Working the New ACT Math Probability Items
In the previous post, we divided the probability items found in the last two Preparing-for-the-ACT Guides into three categories. In this post, we work those items. If you have questions or comments, shoot me an email at firstname.lastname@example.org.
These items are provided to give you examples of the ways you can expect ACT to test probability. These are screenshots from the ACT’s booklets, not the property of 36 University.
Item Type 1: Basic Probability Items
These items require you to apply the basic probability formula:
P(A) = (# of events corresponding to A/ total # of possible events)
Step 1) Recognize there are now 755 pieces.
Step 2) Of those 775 pieces, 5 are the new “extra” pieces.
Step 3) Use probability formula: P(extra piece) = 5/755
Step 1) Current probability of red marble: 12/32
Step 2) Recognize we need a fraction that will reduce to 3/5, so the denominator has to reduce to 5.
Step 3) Begin adding red marbles in increments so that the total number of red marbles is divisible by 3.
Current Probability of red: 12/32 –> 3/8
Add 3 red marbles. Updated probability of drawing red marble: 15/35 –> 3/7
Add 8 red marbles. Updated probability of drawing red marble: 20/40 –> 1/2
Add 13 red marbles. Updated probability of drawing red marble: 25/45 –> 5/9
Add 18 red marbles. Updated probability of drawing red marble: 30/50 –> 3/5. (I should have known!)
Item Type 2: Probability from Graphs
These items require you to utilize your graph reading skills and basic probability concepts.
Step 1) They provide formula for odds. Odds = in the age range:not in the age range.
Step 2) Percentage of persons in 25-35 years range: 42% or 42 out of 100.
Step 3) If 42 out of 100 are in the age range, the other 58 must not be in the age range.
Step 4) Set up the odds. 42:58 –> 21:29
Step 1: P(Type A or Type AB blood) = (# of Type A + # of Type AB)/ (Total # of possibilities)
Step 2: P(Type A or Type AB blood) = (67 + 6)/150 –> 73/150
Item Type 3: Probability of Multiple Events
Multiple events probability items ask you take one additional step. Often, that means you’ll just need to multiply the probabilities of each event. Here are examples:
Step 1: 80% pass written test. Of 1,000, we expect 800 to pass written test. (80% • 1000)
Step 2: Of those that pass written test, 60% pass driving test. 60% • 800 that passed written –> 480 expected to pass both
Step 1: Chances of guessing a particular item correctly is 1/3, since there are three answer choices.
Step 2: Chances of guessing all 4 items correctly? Multiply the probabilities: (1/3) • (1/3) • (1/3) • (1/3) –> 1/81
Wrapping It Up
We hope these solutions helped you work these items more efficiently! If you have an alternative, quicker method to solving any of these items, we’d love to see it.
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