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Neporo4naja [7]
3 years ago
14

Use the Venn diagram to calculate probabilities

Mathematics
2 answers:
Shkiper50 [21]3 years ago
8 0

From the Venn diagram, we can gather that there are 35 total objects (6 in both A and B; 15 in A but not B; 10 in B but not A; and 4 in neither A nor B), and we have the probabilities

\mathbb P(A\cap B)=\dfrac6{35}

\mathbb P(A)=\dfrac{15+6}{35}=\dfrac{21}{35}=\dfrac35 (this is the answer)

\mathbb P(B)=\dfrac{10+6}{35}=\dfrac{16}{35}

By definition of conditional probability,

P(A\mid B)=\dfrac{P(A\cap B)}{P(B)}=\dfrac{\frac6{35}}{\frac{16}{35}}=\dfrac6{16}=\dfrac38

P(B\mid A)=\dfrac{P(B\cap A)}{P(A)}=\dfrac{\frac6{35}}{\frac{21}{35}}=\dfrac6{21}=\dfrac27

Norma-Jean [14]3 years ago
7 0

The answer is 3/5

21/35=3/5=P(A)


A is the correct answer

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