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djverab [1.8K]
3 years ago
9

Use the Venn diagram to calculate probabilities. Circles A and B overlap. Circle A contains 15, circle B contains 10, and the in

tersection contains 6. Number 4 is outside of the circles. Which probability is correct?

Mathematics
1 answer:
grin007 [14]3 years ago
8 0

Answer:

(B) P(B)=\dfrac{16}{31}

Step-by-step explanation:

From the Venn diagram, n(AUB)=31

The given probabilities in the option are calculated below:

P(A)=\dfrac{21}{31}\\\\P(B)=\dfrac{16}{31}\\\\P(A|B)=\dfrac{P(A\cap B)}{P(B)}= \dfrac{6/31}{16/31} =\dfrac{6}{16}=\dfrac{3}{8} \\\\P(B|A)=\dfrac{P(B\cap A)}{P(A)}= \dfrac{6/31}{21/31} =\dfrac{6}{21}=\dfrac{3}{7}

The only correct option is the probability of B which is \frac{16}{31}

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