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Tanya [424]
3 years ago
12

If P(A)=2/3, P(B)=4/5, and P(A U B) =11/15, what is P(A ∩ B)?

Mathematics
2 answers:
Evgen [1.6K]3 years ago
7 0

Answer:

P(A ∩ B) = \frac{11}{15}

Step-by-step explanation:

If P(A)=2/3, P(B)=4/5, and P(A U B) =11/15

we need to find out  P(A ∩ B)

P(A U B) = P(A) + P(B) - P(A ∩ B)

Now we add P(A ∩ B) on both sides and subtract P(A U B) from both sides

P(A ∩ B) = P(A) + P(B)- P(A U B)

now we plug in the values

P(A ∩ B) = \frac{2}{3} + \frac{4}{5} - \frac{11}{15}

Make the denominators same . LCD  is 15

P(A ∩ B) = \frac{10}{15} + \frac{12}{15} - \frac{11}{15}

P(A ∩ B) = \frac{22}{15}-\frac{11}{15}

P(A ∩ B) = \frac{11}{15}

Juliette [100K]3 years ago
3 0
The answer is A on apex 
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Answer:

Step-by-step explanation:

Hello!

A: "Method A is used" and the probability of using it is P(A)= 0.75

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If you were to put all possible options in a contingency table:

A B Total

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You can easily notice that the probability of learning the skill is the sum of the probabilities of "learning the skill and using method A" plus "learning the skill and using method B" These two intersections are unknown so first you apply the formula of conditional probability to find them out:

P(L/A)= P(A∩L)/P(A) ⇒ P(A∩L)= P(A)*P(L/A)= 0.75*0.80= 0.6

P(L/B)= P(B∩L)/P(B) ⇒ P(B∩L)= P(B)*P(L/B)= 0.25*0.95= 0.2375

P(L)= P(A∩L) + P(B∩L)= 0.6 + 0.2375= 0.8375

Correct option: e.P(L) = .75 * .80 + .25 * .95 = .8375

I hope you have a SUPER day!

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