Please help me with an addition formula problem!

1 answer:

6 0

2a + 3b = 6
5a + 2b = 4

We multiply the first equation by 5 and the second by 2 and and subtract the second from the first:

10a + 15b = 30
-10a -4b = -8

11b = 22
b = 2

2a + 3(2) = 6
2a = 0
a = 0

Checking,
5(0) + 2(2) = 4
4 = 4, true

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Answer:

a) 0.54 = 54% probability that a randomly selected person will feel guilty for either wasting food or leaving lights on when not in a room or both.

b) 0.46 = 46% probability that a randomly selected person will not feel guilty for either of these reasons

Step-by-step explanation:

We use Venn's Equations for probabilities.

I am going to say that:

P(A) is the probability that a randomly selected person will feel guilty about wasting food.

P(B) is the probability that a randomly selected person will feel guilty about leaving lights on when not in a room.

0.12 probability that a randomly selected person will feel guilty for both of these reasons.

This means that $P(A \cap B) = 0.12$

0.27 probability that a randomly selected person will feel guilty about leaving lights on when not in a room.

This means that $P(B) = 0.27$

0.39 probability that a randomly selected person will feel guilty about wasting food

This means that $P(A) = 0.39$

a. What is the probability that a randomly selected person will feel guilty for either wasting food or leaving lights on when not in a room or both (to 2 decimals)?

$P(A \cup B) = P(A) + P(B) - P(A \cap B) = 0.39 + 0.27 - 0.12 = 0.54$