I understand how the problem becomes "What is the probability of getting exactly 3 heads in 5 flips of a coin?

I don't understand how a total of 32 possible outcomes exist.

From Barron's SAT Subject test math level 2

  • $\begingroup$ 1. There are five flips left, and you're interested in whether you get exactly three of these five as heads. 2. In real life, witnessing the first 5 flips as heads, one would seriously doubt if the flips are actually random. $\endgroup$ – vadim123 Nov 7 '14 at 22:10
  • $\begingroup$ The next 5 flips can each take on 2 outcomes, multiplying these together give a total of $2^5=32$ combinations. $\endgroup$ – Graham Kemp Nov 7 '14 at 22:11

At least you've avoided the cliffs of not understanding independence of coin tosses successfully. A total of $32=2^5$ outcomes exists because each of the five remaining coins might be heads or tails. Only $5\choose 3$ of these outcomes are "good", thus the probability in question is $\frac{5\choose 3}{2^5}=\frac5{16}$.


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