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Math  /  Data & Statistics

Question∨1\vee 1 12 3 4 5 6 ✓7\checkmark 7 78
If P(A)=0.51,P(B)=0.6P(A)=0.51, P(B)=0.6, and P(AP(A and B)=0.41B)=0.41, find P(AP(A or B)B). P(A or B)=P(A \text { or } B)= □\square □\square

Studdy Solution

STEP 1

1. P(A)=0.51 P(A) = 0.51 is the probability of event A A .
2. P(B)=0.6 P(B) = 0.6 is the probability of event B B .
3. P(A and B)=0.41 P(A \text{ and } B) = 0.41 is the probability of both events A A and B B occurring simultaneously.
4. We are using the formula for the probability of the union of two events: P(A or B)=P(A)+P(B)−P(A and B) P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B) .

STEP 2

1. Identify the given probabilities.
2. Apply the formula for the probability of the union of two events.
3. Calculate P(A or B) P(A \text{ or } B) .

STEP 3

Identify the given probabilities:
P(A)=0.51,P(B)=0.6,P(A and B)=0.41 P(A) = 0.51, \quad P(B) = 0.6, \quad P(A \text{ and } B) = 0.41

STEP 4

Apply the formula for the probability of the union of two events:
P(A or B)=P(A)+P(B)−P(A and B) P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B)

STEP 5

Substitute the given values into the formula:
P(A or B)=0.51+0.6−0.41 P(A \text{ or } B) = 0.51 + 0.6 - 0.41

STEP 6

Perform the calculation:
P(A or B)=1.11−0.41=0.70 P(A \text{ or } B) = 1.11 - 0.41 = 0.70
The probability P(A or B) P(A \text{ or } B) is:
0.70 \boxed{0.70}

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