The binomial distributionEdexcel A-Level Maths: Mind map

Exam questions on The binomial distribution

1. A student guesses the answer to every question on a 10-question multiple-choice test. Each question has four options, exactly one of which is correct. The random variable $X$ is the number of questions answered correctly, and $X\sim B(10,0.25)$.
   Find $P(X\ge4)$.2 marks
2. A gardener plants 12 seeds. Each seed germinates with probability $0.9$, independently of the others. The random variable $Y$ is the number of seeds that germinate.
   Find $P(Y=10)$.2 marks
3. A machine produces bolts. Each bolt is defective with probability $0.05$, independently of the others. Bolts are packed in samples of 20, and $X$ is the number of defective bolts in a sample.
   State the distribution of $X$ and find the probability that a sample contains exactly 2 defective bolts.3 marks