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$($($X\le4$X≤4$|$|$X\ge2$X≥2$)$).
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.