Question

If P(A) = 1/3, P(B) = 2/5, and P(A ∪ E) = 3/5; what is P(A ∪ E)?

a) 1/5
b) 3/15
c) 2/5
d) 1/3

Answer 1

To find P(A ∪ E), we can use the formula P(A ∪ E) = P(A) + P(E) - P(A ∩ E). Given that P(A) = 1/3, P(E) = ?, and P(A ∪ E) = 3/5, we need to find P(E) and P(A ∩ E). By rearranging the formula and solving for P(A ∩ E), we find that P(A ∩ E) = 1/15. Substituting this value back into the equation allows us to find that P(E) = 5/15. Therefore, P(A ∪ E) = 1/3 + 5/15 - 1/15 = 3/15.

Step-by-step explanation:

To find P(A ∪ E), we can use the formula:

P(A ∪ E) = P(A) + P(E) - P(A ∩ E)

Given that P(A) = 1/3, P(E) = ?, and P(A ∪ E) = 3/5, we need to find P(E) and P(A ∩ E).

We can rearrange the formula to solve for P(E):

P(E) = P(A ∪ E) - P(A) + P(A ∩ E)

Substituting the given values:

P(E) = 3/5 - 1/3 + P(A ∩ E)

Since the sum of probabilities must equal 1, we have:

p = 3/5 - 1/3 + P(A ∩ E)

Simplifying the equation and solving for P(A ∩ E):

P(A ∩ E) = 1 - 3/5 + 1/3

P(A ∩ E) = 5/15 - 9/15 + 5/15

P(A ∩ E) = 1/15

Now we can substitute the value of P(A ∩ E) back into the equation to find P(E):

P(E) = 3/5 - 1/3 + 1/15

P(E) = (9/15) - (5/15) + (1/15)

P(E) = 5/15

Therefore, P(A ∪ E) = P(A) + P(E) - P(A ∩ E) = 1/3 + 5/15 - 1/15 = 3/15