Question 1

given the following information about events a, b, and c, determine which pairs of events, if any, are independent and which pairs are mutually exclusive.

p(a)=0.26 , p(b)=0.5 , p(c)=0.45 . p(a|b)=0.26 , p(b|c)= 0 , p(c|a)=0.26

select all correct answers.

select all that apply:

b and c are independent
a and c are mutually exclusive
a and b are independent
a and c are independent
b and c are mutually exclusive
a and b are mutually exclusive

question 2

let e be the event that a randomly chosen person exercises. let d be the event that a randomly chosen person is on a diet. identify the answer which expresses the following with correct notation: of all the people who exercise, the probability that a randomly chosen person is on a diet.

select the correct answer below:

p(d) and p(e)
p(e and d)
p(e|d)
p(d|e)

Answer with Step-by-step explanation:

1.We are given that  three events  A, B and C.

P(A)=0.26

P(B)=0.5

P(C)=0.45

P(A/B)=0.26

P(B/C)=0

P(C/A)=0.26

When two events A and B are independent then

If two events are mutually exclusive then

We know that

Hence,

Therefore, event A and B are independent.

Therefore, events B and C are mutually exclusive.

Hence, event A and C are neither independent nor mutually exclusive.

A and B are independent

B and C are mutually exclusive.

2.Let E be the event that  randomly chosen person exercises and D be the event that a randomly chosen person is on a diet.

According to question

We have to find P(D/E).

Answer : P(D/E)

answer:   28.56 feet (approx)

step-by-step explanation:

since, triangle abc has measure of angle c equal to 55 degrees, measure of angle abc equal to 90 degrees, and length of bc equal to 20 feet.

we have to find out the measurement of segment ab.

therefore, tan 55° =

but bc = 20 feet.

⇒ tan 55 ° =  

⇒ ab = 20 × tan 55 °

⇒ ab = 20 × 1.42814800674

⇒ ab = 28.5629601348   ≈ 28.56 feet