Additional Topics in Probability and Counting

A child is drawing a rainbow using a box of sixteen different colored crayons, which include the seven required colors. After drawing the red, orange, yellow, and green arcs in the proper order, she forgets the last three colors. From the remaining twelve crayons, she chooses three at random to finish drawing the rainbow. What is the probability that she correctly finishes the ROYGBIV rainbow?

• 1/792

• 1/45

• 1/42

• 1/320

A shipment of fourteen smartphones contains five with cracked screens. If sold in a random order, what is the probability that the first nine sold have undamaged screens?

• 1/2002

• 1/165

• 1/56

• 1/3003

How many are in set A or B?

• 16

• 13

• 20

• 53

How many are in set A and B?

• 16

• 13

• 20

• 53

Katie has 6 hair scrunchies (2 red, 3 green and 1 pink) that she will put on her pony tail.  In how many ways can she arrange these?

• 6

• 12

• 60

• 720

How many arrangements of answers are possible for a true/false test with 10 questions?

• 1024

• 100

• 20

• 10

In how many different ways can first, second, and third prize winners be chosen in a random drawing if 50 people entered a contest?

• 50

• 19600

• 117600

• 150

Two fair dice are rolled, determine the probability that the sum of the two dice is 11.

• 2/12

• 2/36

• 11/36

• 11/12

What is the probability of spinning red?

• 0

• 5/12

• 1/2

• 3/4

Heather must choose a PIN code for her ATM card.  The pin is a 4 digit code.  How many possible PIN numbers are there?

• 10,000

• More than 1 million

• 4

• None of these