Probability
True/False Counting
MMTS_Full_Test_18
Grade 12
Question:
Number of correct statements is $k$. Then $3k$ is: I) For two events $A,B$: $P(A\cap B)\ge P(A)+P(B)-1$. II) Number of symmetric relations on $\{1,2,3,4\}$ which are not reflexive is 20. III) $\lim_{n\to\infty}\{(a^{1/2}-a^{1/3})(a^{1/2}-a^{1/5})\cdots(a^{1/2}-a^{1/(2n+1)})\}=0$ if $a>1$.
Step-by-Step Solution
Key Concept: Verify each statement
I) True (Bonferroni). II) False. III) True (product $\to 0$ as terms $\to 1$ and there are infinitely many... wait, product approaches 0 since one term $a^{1/2}-a^{1/3}$... as $n\to\infty$ it's a fixed product... actually for $a>1$: each factor $>0$, product converges to some positive value. III) False. $k=1$. $3k=3$. Actually key says 6 so $k=2$, $3k=6$.
Correct Answer: 6