(a) To determine P∪BC, given that B and C are independent, we can use the formula P(A∪B) = P(A) + P(B) - P(A∩B).

Since B and C are independent events, P(B∩C) = P(B) * P(C).

Given that P(B) = 0.37 and P(C) = 0.48, we can substitute these values into the formula:

P(B∩C) = 0.37 * 0.48 = 0.1776.

Now, we can calculate P∪BC:

P∪BC = P(B) + P(C) - P(B∩C)
= 0.37 + 0.48 - 0.1776
= 0.6724.

Therefore, P∪BC is equal to 0.6724.

(b) To determine P∪BC, given that B and C are mutually exclusive, we can use the formula P(A∪B) = P(A) + P(B).

Since B and C are mutually exclusive events, P(B∩C) = 0.

Given that P(B) = 0.37 and P(C) = 0.48, we can substitute these values into the formula:

P∪BC = P(B) + P(C)
= 0.37 + 0.48
= 0.85.

Therefore, P∪BC is equal to 0.85.

Question

(a) To determine P∪BC, given that B and C are independent, we can use the formula P(A∪B) = P(A) + P(B) - P(A∩B).

Since B and C are independent events, P(B∩C) = P(B) * P(C).

Given that P(B) = 0.37 and P(C) = 0.48, we can substitute these values into the formula:

P(B∩C) = 0.37 * 0.48 = 0.1776.

Now, we can calculate P∪BC:

P∪BC = P(B) + P(C) - P(B∩C)
       = 0.37 + 0.48 - 0.1776
       = 0.6724.

Therefore, P∪BC is equal to 0.6724.

(b) To determine P∪BC, given that B and C are mutually exclusive, we can use the formula P(A∪B) = P(A) + P(B).

Since B and C are mutually exclusive events, P(B∩C) = 0.

Given that P(B) = 0.37 and P(C) = 0.48, we can substitute these values into the formula:

P∪BC = P(B) + P(C)
       = 0.37 + 0.48
       = 0.85.

Therefore, P∪BC is equal to 0.85.

Knowee AI · Accepted Answer

(a) To determine P∪BC, given that B and C are independent, we can use the formula P(A∪B) = P(A) + P(B) - P(A∩B).

Since B and C are independent events, P(B∩C) = P(B) * P(C).

Given that P(B) = 0.37 and P(C) = 0.48, we can substitute these values into the formula:

P(B∩C) = 0.37 * 0.48 = 0.1776.

Now, we can calculate P∪BC:

P∪BC = P(B) + P(C) - P(B∩C)
       = 0.37 + 0.48 - 0.1776
       = 0.6724.

Therefore, P∪BC is equal to 0.6724.

(b) To determine P∪BC, given that B and C are mutually exclusive, we can use the formula P(A∪B) = P(A) + P(B).

Since B and C are mutually exclusive events, P(B∩C) = 0.

Given that P(B) = 0.37 and P(C) = 0.48, we can substitute these values into the formula:

P∪BC = P(B) + P(C)
       = 0.37 + 0.48
       = 0.85.

Therefore, P∪BC is equal to 0.85.

Let B and C be two events such that =PB0.37 and =PC0.48.Do not round your responses. (If necessary, consult a list of formulas.)(a) Determine P∪BC, given that B and C are independent.(b) Determine P∪BC, given that B and C are mutually exclusive.