Probability
Experiment II success probability
MJAT_TS8_P2
Grade 12
Question:
In Experiment I, two colored unbiased coins are tossed. Two subsets $P$ and $Q$ of 2 elements each are chosen randomly from sample space $S$ with replacement. In Experiment II, the same coins are tossed; the experiment is successful if the outcome matches any element of $P$ or $Q$. The probability that Experiment II is NOT successful is:
A) $\dfrac{1}{2}$
B) $\dfrac{1}{6}$
C) $\dfrac{1}{4}$
D) $\dfrac{1}{3}$
Step-by-Step Solution
Key Concept: Sample space $S=\{HH,HT,TH,TT\}$, $|S|=4$. $P,Q$ each have 2 elements. $P(\text{not successful})=P(\text{outcome}\notin P\cup Q)$.
Answer: **C** ($1/4$).
Correct Answer: C