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Probability — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsProbability1 Mark
Question
A coin is tossed three times, determine P(E|F),
where E: Head on third toss, and F: Head on first two tosses.
✓

Answer

The sample space of the given experiment will be:
S = {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}
Here, E: head on third toss 
And F: head on first two tosses
⇒ E = {HHH, HTH, THH, TTH} and F = {HHH, HHT}
⇒ E ∩ F = {HHH}
So, P(E) = $\frac{4}{8}=\frac{1}{2}$, P(F) = $\frac{2}{8}=\frac{1}{4}$, $\mathrm{P}(\mathrm{E} \cap \mathrm{F})=\frac{1}{8}$ 
$\text{Now, we know that}~P(E | F)=\frac{P(E \cap F)}{P(F)}$ 
$\Rightarrow P(E | F)=\frac{\frac{1 }{ 8}}{\frac{1}{ 4}}=\frac{4}{8}=\frac{1}{2}$ 
$\Rightarrow P(E | F)=\frac{1}{2}$

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