Question

Determine $P\left(\frac{E}{F}\right)$
A coin is tossed three times
E: Atleast two heads F : atmost two heads

Answer 1

Here, E : set of events in which atleast two heads occur and F: set of events in which atmost tow heads occur.
$\therefore E=(HHH,HHT,HTH,THH)$
[Here, we consider the cases of two and three heads, as the condition given is atleast not atmost]
F = (TTT, THT, TTH, HTT, HHT, HTH, THH,)
$\Rightarrow (E\cap F)=(HHT,HTH,THH)$
Hence $P\left(E\right)=\frac{Numberoffavourableoutcomes}{Totalnumberofoutcomes}=\frac{4}{8}=\frac{1}{2}SimilarlyP\left(F\right)=\frac{7}{8}andP(E\cap F)=\frac{3}{8}\therefore P\left(\frac{E}{F}\right)=\frac{P(E\cap F)}{P\left(F\right)}=\frac{\frac{3}{8}}{\frac{7}{8}}=\frac{3}{8}\times \frac{8}{7}=\frac{3}{7}$