Tree-diagram probability for two-stage experiments
A chance experiment first chooses a sleeve and then chooses one card from that sleeve
The first table gives the first-stage choice counts. The second table gives the card counts for each first-stage choice
| First-stage choice | Count |
|---|---|
| Sleeve R | 7 |
| Sleeve P | 3 |
| First-stage choice | black | blue | white | Row total |
|---|---|---|---|---|
| Sleeve R | 3 | 7 | 4 | 14 |
| Sleeve P | 7 | 3 | 7 | 17 |
The ordered outcomes form the sample space \(S\). Let \(E\) be the event that at least one of these is true: the first choice is Sleeve P; the final card is white
Each first-stage count represents that many equally likely selection tickets. After choosing a source, select one of its items uniformly at random. Calculate the missing probabilities marked ? from these counts
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