Mathematics 9709 · AS & A Level · Discrete random variables

Discrete random variables — practice question

Alisha owns four coins. One of them is biased so that the probability of getting a head is $0.6$. The other three coins are fair. Alisha tosses all four coins at the same time. The random variable $X$ represents the number of heads obtained.
(a)[3]

Show that the probability of getting exactly one head is $0.225$.

(b)[2]

Complete the probability distribution table for $X$, with $x = 0, 1, 2, 3, 4$ and entries such as $P(X = 0) = 0.05$, $P(X = 1) = 0.225$ and $P(X = 4) = 0.075$ already provided.

(c)[2]

Given that $\text{E}(X) = 2.1$, find $\mathrm{Var}(X)$.

Worked solution & mark scheme

This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: Correct probability expression, for example $0.6(0.5)^3 + 0.4(0.5)^3\times 3$

  • Full mark scheme, point by point
  • Step-by-step worked solution
  • Write your answer & get it marked instantly by AI