Comparing multiple representations to calculate conditional probabilities

12 questions

1. The probability of an outcome occurring given that another event has occurred is called ___ probability.
2. Sam asks 30 pupils if they take GCSE Art (A), GCSE Drama (D) or GCSE Music (M). The frequencies are shown in the Venn diagram. Find P(A ⋃ M).
3. Sam asks 30 pupils if they take GCSE Art (A), GCSE Drama (D) or GCSE Music (M). The frequencies are shown in the Venn diagram. Find P(A ∩ M ∩ D').
4. Here is a frequency Venn diagram. P(A ⋃ B ⋃ C) = ___. Give your answer as a decimal.
5. Here is a frequency Venn diagram. P(A ⋃ C′) = ___. Give your answer as a decimal.
6. This frequency Venn diagram has 80 outcomes altogether. P(A ∩ B ∩ C) = \frac{1}{20}, P(A | B) = \frac{1}{3} and P(A ⋃ B) = 0.7. y = ___.
7. Two spinners are spun once each. The table shows the outcomes for each spinner. Match each value from the frequency tree to its value.
8. An investigation into some rhubarb plants aims to see if using a special fertiliser (F) increases the chance of the plant yielding rhubarb (R). The diagrams show the results. a = ___.
9. An investigation into some rhubarb plants aims to see if using a special fertiliser (F) increases the chance of the plant yielding rhubarb (R). The diagrams show the results. d = ___.
10. An investigation across 60 days explores whether days with rain (R) were more likely to see deer (D) in urban areas. The value of x is ___.
11. An investigation across 60 days explores whether days with rain (R) were more likely to see deer (D) in urban areas. The value of w is ___.
12. A game developer tested to see whether a playable character was more likely to win (W) with a rebalance (R) of the character’s stats or not. P(RW') = ___. Give your answer as a decimal.

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