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Question

A coin is tossed three times, where (A) E: Head on the third toss, F: Heads on the first two tosses. Determine PE|F.


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Solution

Step 1:Finding the value of P(E)and P(F)

When a coin is tossed three times,

Therefore, S={HHH,HHT,HTH,THH,TTH,THT,HTT,TTT}

E : Head On Third Toss

E={HHH,HTH,THH,TTH}

Now, PE=FavourableoutcomeTotaloutcome

PE=48=12

F : Head on the first two tosses.

F={HHH,HHT}

Now, PF=FavourableoutcomeTotaloutcome

PF=28=14

Step 2: Find the PEF

Now, we know that, to find PE|F, we need to find the PEF.

So, EF={HHH}

PEF=18.

We know that, PE|F=PEFPF

PE|F=1814PE|F=48=12

Hence, PE|F=12=0.5.


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