1 A coin is tossed repeatedly until tails has occurred ten t

1. A coin is tossed repeatedly until tails has occurred ten times , what is the probability that, at that point ,heads has not occurred twice in a row?

2.five dice are thrown

a. what is the probability that non of them fall \"one\"?

b.what is the probaility that neither \"one\" nor \"two\" is thrown?

c. what is the probability that \"two\" is the lowest number thrown?

Solution

NOTE: we are suppose to answer one question at a time and for rest of the question repost the question again.

1) Each tail is preceded by h heads.
p(h=0) = 1/2 (i.e. sequence is H)
p(h=1) = 1/4 (i.e. sequence is HT)
p(h>1) = 1/4 (i.e. sequence begins HH)
So for each tail, the probability of not preceding with two head is 3/4.
So for 10 tails, the probability of them all not being preceded by two heads is (3/4)^10