For two events $A$ and $B,$ let $P(A)=0.7$ and $P(B)=0.6.$ Which of the following statement$(s)$ is/are necessarily false?

Consider the $6 \times 6$ square grid in the figure. Let $A_1, A_2, \ldots, A_{49}$ be the points of intersection (dots in the picture) in some order. We say that $A_i$ and $A_j$ are friends if they are adjacent along a row or along a column. Assume that each point $A_i$ has an equal chance of being chosen.
$(1)$ Let $p_i$ be the probability that a randomly chosen point has $i$ many friends,$i=0, 1, 2, 3, 4$. Let $X$ be a random variable such that for $i=0, 1, 2, 3, 4$,the probability $P(X=i)=p_i$. Then the value of $7 E(X)$ is
$(2)$ Two distinct points are chosen randomly out of the points $A_1, A_2, \ldots, A_{49}$. Let $p$ be the probability that they are friends. Then the value of $7 p$ is

If two unbiased six-faced dice are thrown simultaneously until a sum of either $7$ or $11$ occurs,then the probability that $7$ comes before $11$ is

Let $A, B,$ and $C$ be $3$ independent events such that $P(A) = 1/3, P(B) = 1/2,$ and $P(C) = 1/4$. Find the probability that exactly $2$ of the $3$ events occur.

One die has two faces marked $1$,two faces marked $2$,one face marked $3$ and one face marked $4$. Another die has one face marked $1$,two faces marked $2$,two faces marked $3$ and one face marked $4$. The probability of getting the sum of numbers to be $4$ or $5$,when both the dice are thrown together,is

$A$ locker can be opened by dialing a fixed three-digit code (between $000$ and $999$). $A$ stranger who does not know the code tries to open the locker by dialing three digits at random. The probability that the stranger succeeds at the $k^{th}$ trial is