STAT213 Tutorial sheet #3

 

Question 1

a)      A restaurant serves 6 combos. If there is a party of 4 people, what is the sample space? What is the probability of each event in the sample space? (see key)

b)      For the party of 4 people, if at least 2 combos are chosen, what is the probability that at least 3 combos are chosen?

(83.72%)

Question 2

A euchre deck consist of 24 cards: 9, 10, jack, queen, king and ace of each suit. As with poker, each player receives 5 cards.

a)      Compute the probability for each event in the sample space. (There are 6 events; see key for solution)

b)      What is the probability a euchre hand has 3 spades or 2 jacks? (22.19%)

c)      If a player has exactly 2 jacks, what is the probability of each event in the sample space?  (There are 3 events; see key for solution)

 

Question 3

A box has 12 balls: 4 white, 4 red and 4 blue. You draw 3 balls.

a)      Find the probability of drawing one of each colour. (29.09%)

b)      Find the probability of drawing at least 1 blue. (74.55%)

c)      If at least 1 of the 3 balls chosen is red, what is the probability that you drew at least 2 red balls? (31.71%)

 

Question 4

a)      A committee has 14 members. If it needs to fill the president, VP, secretary and treasurer positions from among the 14, how many ways can the positions be filled? (24,024)

b)      Suppose the committee had to choose 3 people to go on a business trip. How many ways can they choose the 3 people? (364)

c)      Suppose the committee has 6 senior members and 8 junior members. If at least 1 of the 3 people going on the trip must be a senior member, how many ways can they be chosen? (308)

 

Question 5

a)      Suppose a 4-digit alphanumeric password can be filled with either numbers or letters (not case-sensitive). How many passwords can be created if none of the letters or numbers can be repeated? (1,413,720)

b)      Same situation as part a, but the first digit must be a letter. (1,021,020)