Answer:
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
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.