Please could someone verify if my proposed solutions stack up correctly for the following questions?
Consider the tossing of two fair coins:
a) Compute the probability of at least one head and a match or both?
Sol: the sample set of outcomes will be {(HH),(HT),(TH),(TT)}.
Pr(atLeastOneHead) = 3/4 = 0.75
Pr(match) = 2/4 = 0.5
Pr(both) = 3/4 + 1/2 – 1/4 = 1
b) What is the conditional probability of obtaining two heads when flipping a coin twice given that at least one head was obtained?
Using the sample space => {(HH),(HT),(TH),(TT)}. The pr(atLeastOneHeadObtained)
= 3 out of the four outcomes = 3/4
Pr((twoHeadsObtainted) n (atLeastOneHeadObtained)) = 1/4
The conditional probability = .25 / .75
c) Are the events that at least one head shows and a match statistically independent?
Two events are independent if P(AnB) = P(A).P(B).
P(AnB) = 1/4
P(A) * P(B) = 1/2 * 1/2 = 1/4
Therefore, the events are statistically independent
Thanks in advance
Best Answer
a) Wrong answer. In calculating $P(A \cup B)$, you need to use the principle of Inclusion and Exclusion which states that
$$P(A \cup B) = P(A) + P(B) - P(A \cap B)$$
b) Correct answer. Correct approach.
c) Wrong answer. Correct approach. Calculate $P( A \cap B)$ again, it is not 0. For example, it is possible to have at least 1 head AND get a match of the coins? (This might tie back to part a.)