We have a small deck of ten cards. Four of the cards have the number 1 on them, three cards
have the number 2, two cards have the number 3 and one card has the number 4. We will shuffle
the deck and randomly select two of the cards (without replacement). (a) The outcome of
interest is the number on each of the two cards we select. List the complete sample space of
outcomes. (b) What is the probability of selecting two of the same number? (c) What is the
probability that the number on the second selected card is greater than the number on the first
selected card? (d) Let X be the minimum of the two numbers on the selected cards. Find the
probability distribution of X. (e) What is the probability that X = 2 if no 3\'s are selected? (f)
Find the expected value of X. (g) Find the variance of X.
Solution
Four of the cards have the number 1 on them, three cards have the number 2, two
cards have the number 3 and one card has the number 4. We will shuffle the deck and randomly
select two of the cards (without replacement). (a) The outcome of interest is the number on each
of the two cards we select. List the complete sample space of outcomes. The sample space has 10
ways to list the 1st number of the pair and 9 ways to list the 2nd number of the pair. So it has 90
pairs. I\'m not go list all those but you should so you can figure out the answers to b,c,d, etc..
We have a small deck of ten cards. Four of the cards have the numbe.pdf
1. We have a small deck of ten cards. Four of the cards have the number 1 on them, three cards
have the number 2, two cards have the number 3 and one card has the number 4. We will shuffle
the deck and randomly select two of the cards (without replacement). (a) The outcome of
interest is the number on each of the two cards we select. List the complete sample space of
outcomes. (b) What is the probability of selecting two of the same number? (c) What is the
probability that the number on the second selected card is greater than the number on the first
selected card? (d) Let X be the minimum of the two numbers on the selected cards. Find the
probability distribution of X. (e) What is the probability that X = 2 if no 3's are selected? (f)
Find the expected value of X. (g) Find the variance of X.
Solution
Four of the cards have the number 1 on them, three cards have the number 2, two
cards have the number 3 and one card has the number 4. We will shuffle the deck and randomly
select two of the cards (without replacement). (a) The outcome of interest is the number on each
of the two cards we select. List the complete sample space of outcomes. The sample space has 10
ways to list the 1st number of the pair and 9 ways to list the 2nd number of the pair. So it has 90
pairs. I'm not go list all those but you should so you can figure out the answers to b,c,d, etc.
