Simple question I may be over thinking
30. Gift Baskets: The Gift Basket Sore had the following premade gift baskets containing the following combinations in stock.
cookies mugs candy
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coffee 20 13 10
tea 12 10 12
Choose 1 basket at random. Find the probability that it contains
a. Coffee or candy
b Tea given that it contains mugs
c. Tea and cookies
a. I got 5/7 or .71
b. 10/77 or .13
c. I got 12/77 but I think it's wrong,don't I multiply? - For example:
(20/77)x(12/77)x(10/77)x(12/77) = .0008 or so?
a. Ok
b. 10/23
C. 12/77
(a) total no of coffee we have = 20+13+10=43
total candy = 34
total coffee candy we have are =10
remember or means additon so we will use addition rule here
p(a)+p(b)-p(a intersection b)
so that ; 43/77 + 22/77 - 10/77 = 55/77 or 0.714 Ans
(b) total mugs =23
but mugs containing tea are =10
so by basic probability formula we have favorable events/total sample space.
10/23 or 0.434 Ans.
(c) total cookies 32 and total tea in numbers =34
but we need to find the probability of tea and cookies at the same time
Answer will be 12/77 or 0.1558.
another solution can be that
as it include and word it may refers to multiplication formula with that we have the following solution
formula = p(a).p(b)
total tea= 34
total cookies= 32/77 x 43/77 = 1088/5929 or 0.1836 Ans
well i am not sure about this solution.tell me if someone knows
a. Oh, coffee or candy, what a dilemma! Well, let's see. We have 20 baskets with coffee and 10 baskets with candy, out of a total of 77 baskets. So, we can add those up and get a probability of 30 baskets out of 77, which simplifies to 15/38 or approximately 0.39. So close, yet so far.
b. Ah, the elusive tea, hiding behind those mugs! We have 10 baskets with mugs and tea, out of a total of 77 baskets. So, the probability of getting tea given that it contains mugs is 10 baskets out of 77, which simplifies to 10/77 or around 0.13. Mugs and tea, a match made in beverage heaven!
c. Tea and cookies, a classic combination indeed! If we’re looking for both tea and cookies together in one basket, we multiply their individual probabilities. So, we have 12 baskets with tea and 20 baskets with cookies, out of a total of 77 baskets. Therefore, the probability of getting tea and cookies together is (12/77) * (20/77), which simplifies to 240/5929 or approximately 0.04. A small but delightful chance, like finding a needle in a haystack made of gift baskets!
a. To find the probability that a randomly chosen gift basket contains coffee or candy, you need to calculate the sum of the probabilities of each individual event occurring. In this case, we need to find the sum of the probability of choosing a basket with coffee and the probability of choosing a basket with candy.
The probability of choosing a basket with coffee is 20/77 (given in the table), and the probability of choosing a basket with candy is 10/77. So, the probability of choosing a basket with coffee or candy is (20/77) + (10/77) = 30/77, which can also be simplified to 10/26 or 5/13.
Therefore, the correct probability for a. is 5/13 or approximately 0.38.
b. To find the probability that a randomly chosen gift basket contains tea given that it contains mugs, you need to divide the probability of choosing a basket with both tea and mugs by the probability of choosing a basket with mugs.
The probability of choosing a basket with mugs is 13/77 (given in the table), and the probability of choosing a basket with both tea and mugs is 10/77 (also given in the table). So, the probability of choosing a basket with tea given that it contains mugs is (10/77) / (13/77) = 10/13.
Therefore, the correct probability for b. is 10/13 or approximately 0.77.
c. To find the probability that a randomly chosen gift basket contains both tea and cookies, you need to multiply the probabilities of choosing a basket with tea and choosing a basket with cookies.
The probability of choosing a basket with tea is 12/77 (given in the table), and the probability of choosing a basket with cookies is 20/77 (also given in the table). So, the probability of choosing a basket with both tea and cookies is (12/77) * (20/77) = 240/5929.
Therefore, the correct probability for c. is 240/5929 or approximately 0.0405. Your initial calculation of 12/77 was correct and there is no need for the additional multiplications.
Let's break down each part of the problem and calculate the probabilities step by step.
a. To find the probability that a random basket contains coffee or candy, we need to calculate the sum of the probabilities of these two events.
- The number of baskets containing coffee is 20.
- The number of baskets containing candy is 10.
- The total number of baskets is 77 (20+13+10+12+10+12).
Therefore, the probability of selecting a basket that contains coffee or candy is: (20+10)/77 = 30/77 ≈ 0.39.
So your calculation of 5/7 or 0.71 is incorrect. The correct probability is approximately 0.39.
b. To find the probability that a basket contains tea given that it contains mugs, we need to find the number of baskets containing both tea and mugs and divide it by the number of baskets containing mugs.
- The number of baskets containing mugs is 13.
- The number of baskets containing tea and mugs is 10.
Therefore, the probability of selecting a basket that contains tea given that it contains mugs is: 10/13 ≈ 0.77.
So your calculation of 10/77 or 0.13 is incorrect. The correct probability is approximately 0.77.
c. To find the probability that a basket contains both tea and cookies, we need to multiply the probabilities of these two events occurring together.
- The number of baskets containing tea is 12.
- The number of baskets containing cookies is 12.
- The total number of baskets is 77.
Therefore, the probability of selecting a basket that contains both tea and cookies is: (12/77) x (12/77) ≈ 0.023.
So your calculation of 12/77 is correct, but you don't need to multiply it by the probabilities of other items. The correct probability is approximately 0.023.
Remember, when calculating probabilities, we usually divide the number of favorable outcomes by the total number of possible outcomes.