When a coin is tossed three times, we have following outcomes

{HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}

Total outcomes =8

A= at least two heads ={HHH, HHT, THH, HTH} = 4

Therefore probability of occurrence of event A = P(A) =

B= at most two heads ={HHT, HTH, HHT, THT, TTH, TTT, HTT} =7

Therefore probability of occurrence of event B = P(B) =

Now Also we want P (A ∩ B) = probability of occurrence of both events A and B

= occurrence of atleast and atmost two heads ={HHT, HTH, THH} =3

Hence, probability of occurrence of both events A and B = P (A ∩ B)=

Therefore, =

= (answer)