The binomial distributionEdexcel International A Level Further Maths: Mind map

Exam questions on The binomial distribution

1. The discrete random variable $X$ has the binomial distribution $\mathrm{B}(12,\,0.25)$.
   Find $\mathrm{P}(X\ge2)$.2 marks
2. A machine makes components. Each component is independently defective with probability $0.04$. A random sample of $20$ components is taken, and the number of defective components in the sample is $X$.
   Find the probability that more than $2$ components in the sample are defective.2 marks
3. A multiple-choice test has $15$ questions. Each question has four options, of which exactly one is correct. A student chooses an option at random for every question, independently. The number of correct answers is $X$.
   Find the probability that the student gets exactly $5$ questions correct.3 marks