Question

After a late night of studying, Ebony decides to grab a latte before class so she can stay awake through her morning lecture. She has only a one-dollar bill, a five-dollar bill, and a ten-dollar bill in her wallet. She pulls one out and looks at it, but then she puts it back. Distracted by a flyer for a new campus organization, she randomly hands a bill from her wallet to the clerk. Construct a sample space, and find the probability that (a)Both bills have the same value.

Answer 1

The questions seem incomplete. To help you, I have been looking for similar question, and found such as below:

After a late night of studying, Ebony decides to grab a latte before class so she can stay awake through her morning lecture. She has only a one-dollar bill, a five-dollar bill, and a ten-dollar bill in her wallet. She pulls one out and looks at it, but then she puts it back. Distracted by a flyer for a new campus organization, she randomly hands a bill from her wallet to the clerk. Construct a sample space, and find the probability that

(a)Both bills have the same value.

(b)Second bill is larger than the first

(c)The value of exactly one bill is odd

(d)The sum of values of both bills is less than $10

Answer:

a) 1/3

b) 1/3

c) 4/9

d) 1/3

Step-by-step explanation:

Sample space:

{1,1}, {1,5}, {1,10}, {5,1}, {5,5}, {5,10}, {10,1}, {10,5}, {10,10}

Note that since the money is put back into her wallet, the event 'looking at the bill' and the event 'hands a bill' will be independent.

For better understanding, it is easier to do it by using tree diagram

a) both bills have the same value

P(same value)

= P(1,1) + P(5,5) + P(10,10)

= (1/3)(1/3) + (1/3)(1/3) + (1/3)(1/3)

= 3(1/9) = 3/9

= 1/3

b) 2nd bill is larger than the first

P(2nd > 1st)

= P(1,5) + P(1,10) + P(5,10)

= 3[(1/3)(1/3)]

= 1/3

c) value of exactly one of the bill is odd

P(only one bill odd)

= P(1,10) + P(5,10) + P(10,1) + P(10,5)

= 4[(1/3)(1/3)]

= 4/9

d) the sum of values of both bills less than 10

P(less than $10)

= P(1,1) + P(1,5) + P(5,1)

= 3[(1/3)(1/3)]

= 1/3