Someone tossed 4 coins.
What is the probabilty that he will get exactly 3 tails when he tosses the 4 coins?
+66 There are actually many ways to solve this problem, but I will show you one I like the best:
There are 2 * 2 * 2 * 2 = 16 possibilities.
We can have 4 possibiltiies that satisfy the problem:
TTTH
TTHT
THTT
HTTT
Thus the answer is 4/16 = 1/4.
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ShockFish
+2668 \({1 \over 2^3} \times {1 \over 2} \times {4 \choose 1} = {4 \over 16} = \color{brown}\boxed {1\over 4}\)
Explanation:
There is a \({1 \over 2} \times {1 \over 2} \times {1 \over 2} \) chance of the successes (\(3\) tails)
There is a \(1 \over 2\) chance of failure (\(1\) head)
There are \(4 \choose 1\) ways to order the failure (the same as \(4 \choose 3\), which counts the ways to order the successes.)
