1. Li rolls a special dice that has 12 sides labeled 1 through 12, then flips a penny. What is the probability, written as a simplified fraction, that she rolls a multiple of 3 and flips tails? 2. A bag contains 5 red marbles, 6 green marbles, and 3 blue marbles. If Cymra draws a marble, puts it back in the bag, then draws another marble, write a multiplication problem you would use to find the probability that both marbles drawn will be red. 3. If Cole flips a coin three times, what is the probability that he will flip three tails in a row? 4. Based on collected data from the past 5 basketball practices, Linda has a 32% for making her free throws. If she shoots 175 more times, how many will she expect to make based on her percentage?

1. The probability that she throws a multiple of 3 and flips tails is 1/6

2. The probability that Cymra draws a red marble put it back and draws a red marble again is 25/196

3.  The probability that Cole flips three tails in a row, P(3T) is 1/8

4. The number of shots Linda is expected to make if she takes 175 shots is 56

Step-by-step explanation:

1. The number of sides on the special die Li rolls = 12 sides

The numbers on the die are 1 through 12

The number of faces on the penny = 2 (heads and tails)

The number of multiples of 3 on the die = 3, 6, 9, and 12 = 4

The probability that she throws a multiple of 3, P(3) = 4/12 = 1/3

The probability that she flips tails rather than heads = 1/2

∴ The probability that she throws a multiple of 3 and flips tails = 1/3 × 1/2 = 1/6

2. The number red marbles in the bag = 5

The number green marbles in the bag = 6

The number blue marbles in the bag = 3

The total number of marbles in the bag = 5 + 6 + 3 = 14

The probability that Cymra draws a red marble put it back and draws a red marble again is given as follows;

The probability with replacement of picking two red marbles = 5/14 × 5/14 = 25/196

3. The probability that Cole flips three tails in a row P(3T) = (1/2)×(1/2)×(1/2) = 1/8

The probability that Cole flips three tails in a row, P(3T) = 1/8

4. The percentage of times Linda makes her free throws in the past 5 basketball practices = 32%

The number of shots she is expected to make if she takes 175 shots = 175 × 32/100 = 56.

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step-by-step explanation: