#### Selection probabilities

What it does

Selection probabilities provides practice at working at the probabilities of selecting, at random, coloured balls from a bag. Each probability is displayed on an appropriate branch of a tree diagram.

The settings

no. red/blue/yellow: set the initial number of balls of each colour in the bag.

total: the total number of balls is automatically displayed.

no. selected: choose the number of balls to be selected (1 or 2)

without: choose whether the selection is “with" or “without" replacement. This option is available only if “no.selected" is set to 2. For the “without" setting, an appropriately coloured ball is crossed out in the second stage to indicate that it has been removed at the first stage and not replaced.

Next “?" probability: enter the probability for the next selection – numerator and denominator - and confirm with “ok". If correct, this fraction will then be displayed in the appropriate location on the tree diagram, otherwise try again.

How to use it

The order in which the probabilities are calculated is as follows.

With “no.selected" set to 1, the three probabilities are calculated in the order from top to bottom on the tree diagram (i.e. red, blue and then yellow).

With “no.selected" set to 2, the three first selections are dealt with first and in the same order as above (i.e. red, blue, yellow) and then the nine secondnd selections are inserted.

For the “without" replacement setting, the second selection probabilities are calculated from top to bottom (on the second branches) of the tree diagram.

For the (with) replacement setting, the second selection probabilities are the same as for the first selection (as any previously removed ball has been replaced) and so the values are automatically inserted into the second branches of the tree diagram.

When all the probabilities have been entered, click in turn on each of the right-most coloured balls on the tree diagram to see the calculation of all nine combined probabilities.

#### Screenshot of Selection probabilities

**There are five movies linked to this applet:**

Explaining the applet:

SelectionProbabilities1

**Using the applet to answer exam questions:**SelectionWithoutReplacement Nick

**SelectionWithReplacement Lara**

**SelectionWithReplacement chess**

**Run the applet ****Selection probabilities**