A teacher frequently forgets his keys. For all n, we note: In the event "on day n, the teacher forgets
his keys", Pn = P(En), Qn = P(En). We assume that: P1 = a is given and that if on day n he forgets his keys,
the next day he forgets them with probability 1/10; if on day n he does not forget his keys, the next day he forgets them
with probability 4/10. Show that Pn+1 =1/10Pn +4/10Qn Deduce a relationship between Pn+1 and Pn What is the
probability of the event “on day n, the teacher forgets his keys”?