Handling Data 5
4 marks · NormalA machine produces three types of screws: Small (S), Medium (M), and Large (L). The probability that a screw is small is 0.2, medium is 0.5, and large is 0.3.
Complete the tree diagram table below showing the probabilities for producing two screws, one after the other, with replacement.
| First screw | Second screw | Probability |
|---|---|---|
| S | S | |
| S | M | |
| S | L | |
| M | S | |
| M | M | |
| M | L | |
| L | S | |
| L | M | |
| L | L |
Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.
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Must show: Complete 9 correct probabilities in the table
Common mistakes: Incorrectly use non-replacement probabilities
Show mark scheme and worked solution
Marking points
M1 · 2 marks · Calculates probabilities for each outcome by multiplying the correct probabilities for each branch (e.g. P(S and S) = 0.2 × 0.2).
A1 · 2 marks · All probabilities in the table are correct and sum to 1.
Worked solution
| First screw | Second screw | Probability |
|---|---|---|
| S | S | 0.04 |
| S | M | 0.10 |
| S | L | 0.06 |
| M | S | 0.10 |
| M | M | 0.25 |
| M | L | 0.15 |
| L | S | 0.06 |
| L | M | 0.15 |
| L | L | 0.09 |