Exam 2 Practice Problems - Solutions

# Exam 2 Practice Problems - Solutions - Physics 6 Spring...

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Physics 6 Spring 2005 Some Practice Problems for Exam 2 SOLUTIONS 1. What is the probability of getting only 2 heads in 4 tosses of a coin? There are 4!/(2!2!)=6 ways to have 2 heads distributed among 4 tosses. You do not need the formula for this; just count the possibilities (HHTT, HTHT, HTTH, THHT, THTH, TTHH). The probability for 2 heads and 2 tails (in any order) is (1/2) 2 (1/2) 2 for one of those orderings. So the overall probability is 6/(2) 4 =6/16=3/8=0.375 2. What is the probability of getting at least 2 heads in 4 tosses of a coin? Add the prob for 2 heads in 4 tosses (from above) to prob for 3 heads in 4 tosses (4!/3!=4 orderings times (1/2) 3 (1/2) 1 or 4/16=1/4) to prob for 4 heads in 4 tosses (1/16). Get 3/8+1/4+1/16=11/16=0.6875 3. Consider 4-sided dice . a. What is the probability of getting exactly 2 number 3's in 4 tosses? 6 orderings (as in (1) above) times (1/4) 2 for two number 3's and (3/4) 2 for two not number 3's OR 6(1/4) 2 (3/4) 2 =54/256=0.211 b. What is the probability of getting at least 2 number 3's in 4 tosses?

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