Valeria has three coins, each of which has a probability of 1/2 of coming up heads. On her first turn, she flips all three coins. If all three come up heads, then she stops. Otherwise, for her second turn, she flips any coins that came up tails. If there are still coins that come up tails, she flips any coins that came up tails, and so on.

Question

(a) What is the probability that Valeria has two heads on her first turn?
(b) What is the probability that Valeria has three heads on her first turn?

(c) What is the probability that Valeria has two heads after her second turn?

(d) What is the probability that Valeria has one head after her second turn?

(e) What is the probability that Valeria has one head after her third turn?

(f) What is the probability that Valeria has three heads after her fourth turn?

Answer 1

a) 1/8
b) 1/8
c) 3/4
d) 3/8
e) 1/4
f) 0