Conditional Probability Example 2

Let three unbiased coins are tossed and E is the event of getting at least 2 head and F  be the event of getting at least 1 tail.

What is P(F/ E)

Answer

Solution:

Method1:

Sample space for E ={HHT, HHH, THH, HTH}

P(E)= 4/8 =1/2

Now For F sample space is {HHT, HHH, THH, HTH} because already E has happened and we have to find F when E has occurred

So P(F/E) =  3/4

 

Method 2:

P(E)= 4/8=1/2

Sample space for (E∩F)={HHT, THH, HTH}

P(E∩F) = 3/8

SO P(F/E)= P(E∩F) / P(E) = (3/8) /(1/2) = 3/4

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