Answer to Question #194522 in Statistics and Probability for slindokuhle

Question

Inside a box are a R10 note, a R20 note, a R50 note and a R100 note. Consider the experiment in which two notes are drawn from the box without replacement. Let 𝑋 be the random variable that gives the value of the smaller (Rands) note. Construct the probability mass function for 𝑋

Answer 1

The total outcomes of drawing two notes from the box =6

They are -{R10,R20},{R10,R50},{R10,R100},{R20,R50},{R20,R100},{R50,R100}

When outcomes are -{R10,R20},{R10,R50},{R10,R100}

$X=10, \text{ and } P(X=10)=\dfrac{3}{6}=0.5$

When outcomes are -{R20,R50},{R20,R100}

$X=20 \text{ and }P(X=20)=\dfrac{2}{6}=0.33$

When outcome is {R50,R100}

$X=50 \text{ and }P(X=50)=\dfrac{1}{6}=0.166$

Therefore the probability mass function for X is as follows: