Question

Помогите с теорией вероятности. В киоске продаются стаканчики мороженого разных видов: шоколадное, пломбир, а также с наполнителями из карамели, вареной сгущенки, черники. Студент для себя и своих друзей покупает наугад 7 стаканчиков мороженого. Какова вероятность, что он купил: а) два пломбира, два шоколадных и три с черникой; б) четыре стаканчика с черничным наполнителем и три с вареной сгущенкой Желательно с решением.

Answer 1

Відповідь:

Пошаговое объяснение:

Покупка любого стаканчика мороженого равновероятна и равна 1/2: купить шоколадное или пломбир, также вероятность купить пломбир одной из добавок или без 1/4

Вероятность купить пломбир с одни из наполнителем 1/2×1/4=1/8

а) р=(1/8)²×(1/2)²× (1/8)= 0,0004882813

б) р=(1/8)⁷=4,76837158E−7

Answer 2

Theory of Probability: Ice Cream Purchase

To solve this problem, we can use the concept of combinations and the formula for calculating the probability of an event.

Calculating the Probability

Total Number of Combinations: The total number of ways the student can choose 7 ice cream cups out of the available flavors can be calculated using combinations. Since there are 5 different flavors, the total number of combinations is given by 5C7.

Calculating the Probability for Each Scenario:

a) Probability of Buying Two Vanilla, Two Chocolate, and Three Blueberry Cups: To calculate the probability of this scenario, we need to find the number of ways the student can choose 2 vanilla, 2 chocolate, and 3 blueberry cups out of the available options.

b) Probability of Buying Four Blueberry Cups and Three Condensed Milk Cups: Similarly, for this scenario, we need to find the number of ways the student can choose 4 blueberry cups and 3 condensed milk cups out of the available options.

Let's calculate the probabilities for each scenario.

Solution

a) Probability of Buying Two Vanilla, Two Chocolate, and Three Blueberry Cups: The probability can be calculated using the formula: \[ P(A) = \frac{n(A)}{n(S)} \] Where: - \( n(A) \) is the number of favorable outcomes for event A. - \( n(S) \) is the total number of possible outcomes.

The number of ways to choose 2 vanilla, 2 chocolate, and 3 blueberry cups can be calculated using combinations.

Number of ways to choose 2 vanilla, 2 chocolate, and 3 blueberry cups: \[ n(A) = \binom{1}{2} \times \binom{1}{2} \times \binom{1}{3} \]

Total number of combinations: \[ n(S) = \binom{5}{7} \]

Now, we can calculate the probability \( P(A) \) for this scenario.

b) Probability of Buying Four Blueberry Cups and Three Condensed Milk Cups: Similarly, we can calculate the probability for this scenario using the same formula and the number of favorable outcomes for event B.

After calculating the probabilities for both scenarios, we can provide the final results.

I will now calculate the probabilities for both scenarios.