The binomial distributionAQA A-Level Maths: Mind map

Exam questions on The binomial distribution

1. A gardener plants 10 seeds. Each seed germinates with probability $0.3$, independently of the others. The number of seeds that germinate is $X$, where $X\sim B(10,0.3)$.
   State two conditions that must hold for $X$ to be modelled by a binomial distribution in this context.2 marks
2. A multiple-choice test has 20 questions, each with four options of which exactly one is correct. A student guesses every answer. The number of correct answers is $X$, where $X\sim B(20,0.25)$.
   Find the probability that the student gets more than 7 questions correct.2 marks
3. A factory makes light bulbs and 8% of them are defective, independently of one another. A box contains 25 bulbs. The number of defective bulbs in a box is $Y$, where $Y\sim B(25,0.08)$.
   Find the probability that a box contains exactly 2 defective bulbs.3 marks