Two professors are applying for grants. ProfessorJane has a probability of 0.62 of being funded. Professor Joe hasprobability 0.25 of being funded. Since the grants are submitted totwo different federal agencies, assume the outcomes for each grantare independent.
1.What is the probability that both professors get their grantsfunded? Give your answer to four decimal places.
2.What is the probability that at least one of the professors will befunded? Give your answer to four decimal places.
3.What is the probability that Professor Jane is funded but ProfessorJoe is not? Give your answer to four decimal places.
4.Given at least one of the professors is funded, what is theprobability that Professor Jane is funded but Professor Joe is not?Give your answer to four decimal places.

1. P(both Professors funded)=0.155

2. P(at least one Professor funded)=0.715

3. P(Jane funded but Joe not funded)=0.465

4. P(Professor Jane is funded but Professor Joe is not/at least one Professor funded)=0.6503

Step-by-step explanation:

P(Professor Jane funded)=P(F1)=0.62

P(Professor Joe funded)=P(F2)=0.25

P(F1')=1-P(F1)=1-0.62=0.38

P(F2')=1-P(F2)=1-0.25=0.75

1.

P(both Professors funded)=P(F1∩F2)

P(both Professors funded)=P(F1)*P(F2)

P(both Professors funded)=0.62*0.25

P(both Professors funded)=0.155

2.

P(at least one Professor funded)=P(F1∪F2)

P(at least one Professor funded)=P(F1)+P(F2)-P(F1∩F2)

P(at least one Professor funded)=0.62+0.25-0.155

P(at least one Professor funded)=0.87-0.155

P(at least one Professor funded)=0.715

3.

P(Jane funded but Joe not funded)=P(F1∩F2')

P(Jane funded but Joe not funded)=P(F1)*P(F2')

P(Jane funded but Joe not funded)=0.62*0.75

P(Jane funded but Joe not funded)=0.465

4.

P(Professor Jane is funded but Professor Joe is not/at least one Professor funded)=P(F1∩F2')/P(F1∪F2)

=P(F1∩F2')∩(F1∪F2)/P(F1∪F2)

=P(F1∩F2')/P(F1∪F2)

P(Professor Jane is funded but Professor Joe is not/at least one Professor funded)=0.465/0.715

P(Professor Jane is funded but Professor Joe is not/at least one Professor funded)=0.6503

x = 10.1

step-by-step explanation:

all of the angles of a tirangle add up to 180º

180 - 65 = 115 (since we already know the value of one angle)

(2x + 7) + (8x + 7) = 115

(combins like terms) 10x + 14 = 115

(isolate the variable subtract 14 from both sides): 10x = 101

(find the variable divide both sides by 10): x = 101/10

x = 10.1

step-by-step explanation:

(s)he  is right it would be 5.5% because it is smaller than 15.5% or anything smaller than 15.5% in general