# If you flip a fair coin 4 times, what is the probability that you will get exactly 2 tails?

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Steve M
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Mar 30, 2017

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# P("Exactly 2H") = 0.375 #

#### Explanation:

**Method 1 - Tree Diagram**

# P("Exactly 2H") = P("HHTT") + P("HTHT") + #

# " " P("HTTH") + P("TTHH") + #

# " " P("THHT") + P("THTH") #

# " " = 0.0625 * 6 #

# " " = 0.375 #

**Method 1 - Combinations**

Using the combination formula:

# ""_nC^r = ( (n), (r) ) = (n!)/(r!(n-r)!) #

We seek any combination of 2 heads from 4 coins:

# n("possible combinations") = ""_2C^4 = ( (4), (2) ) #

# " " = (4!)/(2!(4-2)!) #

# " " = (4!)/(2!2!) #

# " " = (24)/(2*2) #

# " " = 6 #

And the total number of all combinations of 4 flips

# n("total combinations") = 2^4 #

# " " = 16 #

# P("Exactly 2H") = 6/16 #

# " " = 0.375 #

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