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New Zealand
Level 8 - NCEA Level 3

Problems with Discrete Random Variables and Probabilities

Interactive practice questions

Two dice are rolled and the absolute value of the differences between the numbers appearing uppermost are recorded.


Complete the sample space.

    Die $2$2
    1 2 3 4 5 6
Die $1$1 1 $0$0 $\editable{}$ $\editable{}$ $3$3 $\editable{}$ $\editable{}$
2 $1$1 $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$
3 $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $2$2 $\editable{}$
4 $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$
5 $4$4 $\editable{}$ $2$2 $\editable{}$ $\editable{}$ $\editable{}$
6 $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$

Let $X$X be defined as the absolute value of the difference between the two dice. Construct the probability distribution for $X$X using the table below.

Enter the values of $x$x from left to right in ascending order.

$x$x $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$
$P$P$($($X=x$X=x$)$) $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$

Calculate $P$P$($($X<3$X<3$)$).


Calculate $P$P$($($X\le4$X4$|$|$X\ge2$X2$)$).

Approx 8 minutes
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Two earrings are taken without replacement from a draw containing $3$3 black earrings and $5$5 brown earrings.

Let $X$X be the number of black earrings drawn.

An investment scheme advertises the following returns after $2$2 years based on historical probabilities.

A salesperson is starting work in a new region and analyses the probability of how many sales he is likely to make in the next month.



Investigate situations that involve elements of chance: A calculating probabilities of independent, combined, and conditional events B calculating and interpreting expected values and standard deviations of discrete random variables C applying distributions such as the Poisson, binomial, and normal


Apply probability distributions in solving problems

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