SL 4.8—Binomial distribution

The number of trials is $n=25$ bolts, and the probability of success (defective) is $p=0.08$.

Since trials are fixed, independent, with two outcomes and constant probability, $X\sim B(n,p)$ with $n=25$, $p=0.08$.

This gives $X\sim B(25,0.08)$.

The correct notation is $X\sim B(25,0.08)$, option A.

Swaps $n$ and $p$, giving 8 trials with probability 0.25 - incorrect order of parameters.

Uses the probability of failure (0.92) instead of success (0.08) as $p$.

Reverses the order of parameters entirely, writing $p$ before $n$, which is not standard notation.

Only option A correctly assigns $n=25$ and $p=0.08$ in the correct order.

A binomial setup needs fixed trials, two outcomes, constant probability, and independence.

Rolling a die 12 times: $n=12$ is fixed, success = 'rolled a 4', $p=1/6$ constant, rolls are independent.

All four conditions hold, so this is a valid binomial scenario.

Option B is the correct binomial scenario.

Sampling without replacement changes the probability of drawing a spade each time, violating constant probability.

There is no fixed number of trials; the number of days is variable, not fixed.

This is a 'trials until first success' scenario with no fixed $n$, which follows a geometric distribution, not binomial.

Only option B has a fixed $n$, two outcomes, constant $p$, and independence.