Direction. Solve the problem and show complete solution Problem. The following data show the probabilities for the number of milktea sold in a Guinobatan Milktea shop Number of Milk tea 30 35 40 10 15 20 25 45 50 (M) 0 P(M) 0.03 0.025 0.040 0.00 0.150 0.250 0.00 0.140 0.100 0000 0015 1. What is the probability that the number of milk tea sold is more than 25? 2. What is the probability that the number of milk tea sold is at most 157 3. What is the probability that the number of milk tea sold was greater than 5 but less than 35? 4. What is the probability that the number of milk tea sold was at least 25? 5. What is the probability that the number of milk tea sold was less than 40 but greater than 157
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1. To find the probability that the number of milk tea sold is more than 25, we need to add up the probabilities of all the outcomes where the number of milk tea sold is more than 25:
P(number of milk tea sold > 25) = P(30) + P(35) + P(40) + P(45) + P(50)
P(number of milk tea sold > 25) = 0.03 + 0.025 + 0.04 + 0.14 + 0.1
P(number of milk tea sold > 25) = 0.335
Therefore, the probability that the number of milk tea sold is more than 25 is 0.335.
2. To find the probability that the number of milk tea sold is at most 157, we need to add up the probabilities of all the outcomes where the number of milk tea sold is less than or equal to 157:
P(number of milk tea sold ≤ 157) = P(30) + P(35) + P(40) + P(10) + P(15) + P(20) + P(25)
P(number of milk tea sold ≤ 157) = 0.03 + 0.025 + 0.04 + 0 + 0.15 + 0.25 + 0
P(number of milk tea sold ≤ 157) = 0.49
Therefore, the probability that the number of milk tea sold is at most 157 is 0.49.
3. To find the probability that the number of milk tea sold was greater than 5 but less than 35, we need to add up the probabilities of all the outcomes where the number of milk tea sold is greater than 5 and less than 35:
P(5 < number of milk tea sold < 35) = P(10) + P(15) + P(20) + P(25) + P(30)
P(5 < number of milk tea sold < 35) = 0 + 0.15 + 0.25 + 0 + 0.03
P(5 < number of milk tea sold < 35) = 0.43
Therefore, the probability that the number of milk tea sold was greater than 5 but less than 35 is 0.43.
4. To find the probability that the number of milk tea sold was at least 25, we need to add up the probabilities of all the outcomes where the number of milk tea sold is greater than or equal to 25:
P(number of milk tea sold ≥ 25) = P(25) + P(30) + P(35) + P(40) + P(45) + P(50)
P(number of milk tea sold ≥ 25) = 0.25 + 0.03 + 0.025 + 0.04 + 0.14 + 0.1
P(number of milk tea sold ≥ 25) = 0.58
Therefore, the probability that the number of milk tea sold was at least 25 is 0.58.
5. To find the probability that the number of milk tea sold was less than 40 but greater than 15, we need to add up the probabilities of all the outcomes where the number of milk tea sold is less than 40 and greater than 15:
P(15 < number of milk tea sold < 40) = P(20) + P(25) + P(30) + P(35)
P(15 < number of milk tea sold < 40) = 0.25 + 0 + 0.03 + 0.025
P(15 < number of milk tea sold < 40) = 0.305
Therefore, the probability that the number of milk tea sold was less than 40 but greater than 15 is 0.305.