Conditional probability with random variables

A question is this type if and only if it asks to find P(A|B) where A and B are events defined in terms of a discrete random variable.

2 questions

OCR H240/02 Q14
92 marks
14 A random variable \(X\) has probability distribution given by \(\mathrm { P } ( X = x ) = \frac { 1 } { 860 } ( 1 + x )\) for \(x = 1,2,3 , \ldots , 40\).
  1. Find \(\mathrm { P } ( X > 39 )\).
  2. Given that \(x\) is even, determine \(\mathrm { P } ( X < 10 )\). \section*{END OF QUESTION PAPER}
Edexcel S1 2022 October Q7
  1. Adana selects one number at random from the distribution of \(X\) which has the following probability distribution.
\(x\)0510
\(\mathrm { P } ( X = x )\)0.10.20.7
  1. Given that the number selected by Adana is not 5 , write down the probability it is 0
  2. Show that \(\mathrm { E } \left( X ^ { 2 } \right) = 75\)
  3. Find \(\operatorname { Var } ( X )\)
  4. Find \(\operatorname { Var } ( 4 - 3 X )\) Bruno and Charlie each independently select one number at random from the distribution of \(X\)
  5. Find the probability that the number Bruno selects is greater than the number Charlie selects. Devika multiplies Bruno's number by Charlie's number to obtain a product, \(D\)
  6. Determine the probability distribution of \(D\)