Studdy AI Logo
Math

QuestionFind P(B)P(B) given P(A)=0.4P(A)=0.4, P(A or B)=0.95P(A \text{ or } B)=0.95, and P(A and B)=0.3P(A \text{ and } B)=0.3. Round to two decimal places.

Studdy Solution

STEP 1

Assumptions1. The probability of event A, denoted by(A), is0.4. The probability of either event A or event B occurring, denoted by(A or B), is0.953. The probability of both event A and event B occurring, denoted by(A and B), is0.34. The probability of event B, denoted by(B), is what we need to find

STEP 2

We can use the formula for the probability of the union of two events to find(B). The formula is(A or B)=(A)+(B)−(A and B)(A \text { or } B) =(A) +(B) -(A \text { and } B)

STEP 3

We can rearrange this formula to solve for(B):
(B)=(A or B)−(A)+(A and B)(B) =(A \text { or } B) -(A) +(A \text { and } B)

STEP 4

Now, plug in the given values for(A or B),(A), and(A and B) to calculate(B).
(B)=0.95−0.4+0.3(B) =0.95 -0.4 +0.3

STEP 5

Calculate the probability of event B.
(B)=0.95−0.4+0.3=0.85(B) =0.95 -0.4 +0.3 =0.85The probability of event B, rounded to two decimal places, is0.85.

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord