I met the question in my exam:
Flip one coin, the probability of head is $\frac13$, $Pr\{\text{tail}\} = \frac23$. Flip the coin twice, what are the four possible outcomes and their probabilities?
I met the question in my exam:
Flip one coin, the probability of head is $\frac13$, $Pr\{\text{tail}\} = \frac23$. Flip the coin twice, what are the four possible outcomes and their probabilities?
Head Head 1/3 * 1/3 = 1/9 Head Tail 1/3 * 2/3 = 2/9 Tail Head 2/3 * 1/3 = 2/9 Tail Tail 2/3 * 2/3 = 4/9
By the way, the results of 1st and 2nd flips are independent.
Head Head: 1/3 * 1/3 = 1/9 Head Tail: 1/3 * 2/3 = 2/9 Tail Head: 2/3 * 1/3 = 2/9 Tail Tail: 2/3 * 2/3 = 4/9