John tossed a fair coin 3 times. What is the probability that the outcome was “tails” exactly twice?
Choose the correct answer
A) 1/8 B) 1/4 C) 3/8 D) 1/2 E) 9/10
Total number of outcomes = 2*2*2= 
<gadget id="calculator">2*2*2</gadget>
<output>8</output>
8   Number of favorable outcomes= Number of ways two places (for tails) can be chosen out of 3 slots = 3C2 = 3   So probability = 3/8   Alternative   Probability of getting tail in single toss = 1/2   Probability of getting head in single toss = 1/2   Probability of getting First Tail = 1/2   Probability of getting Second tail (Such that first tail has occurred, this incidentally is also the probability when first was head and second is tail) = 1/2 * 1/2 = 1/4   Probability of getting Third Head ( such that first was tail and second was tail) = 1/2 * 1/2 * 12 = 1/8   As you can notice the probability will be 1/8 whatever the sequence of Heads and tails.   We can arrange 2 Tails and one head in 3 ways (33/82 ways OR (3P3)/2! OR enumeration, whichever method you prefer to get here)   Since the favorable even can happen in either of these 3 ways, so Probability = 3 * 1/8 = 3/8   Answer:3/8
<result>C</result>
John tossed a fair coin 3 times. What is the probability that the outcome was “tails” exactly twice?