Question

У Бориса Викторовича в кармане 8 рублёвых, 5 двухрублёвых, 2 пятирублёвые и 1 десятирублёвая монеты. Борис Викторович наугад достаёт монету. Найдите вероятность того, что оставшаяся сумма в кармане составит не менее 36 рублей.

Answer 1

Всего у БВ 8+5+2+1=16 монет и 8*1+5*2+2*5+1*10=38 рублей. Очевидно, что взять 1 монету из 16 можно 16-ю способами. Но благоприятные из них только такие: взять монету в 1 рубль или монету в 2 рубля. Взять монету в 1 рубль можно 8-ю способами, двухрублёвую - 5-ю способами. Таким образом, всего имеем 8+5=13 благоприятных способов из 16. Тогда искомая вероятность P=13/16. Ответ: 13/16  

Answer 2

Calculating the Probability

To calculate the probability of Boris Viktorovich drawing a coin at random and the remaining sum in his pocket being at least 36 rubles, we can use the concept of probability and combinations.

Total Sum in the Pocket

The total sum in Boris Viktorovich's pocket can be calculated by adding up the value of each coin: - 8 ruble coins = 8 * 1 = 8 rubles - 5 two-ruble coins = 5 * 2 = 10 rubles - 2 five-ruble coins = 2 * 5 = 10 rubles - 1 ten-ruble coin = 1 * 10 = 10 rubles

So, the total sum in his pocket is 8 + 10 + 10 + 10 = 38 rubles.

Probability Calculation

To find the probability of drawing a coin at random and the remaining sum being at least 36 rubles, we need to consider the different combinations of coins that would result in a remaining sum of at least 36 rubles.

The possible combinations that would result in a remaining sum of at least 36 rubles are: - Drawing a ten-ruble coin - Drawing a five-ruble coin and a two-ruble coin - Drawing three two-ruble coins

Calculating the Probability

Now, let's calculate the probability for each of these combinations and then sum them up to find the total probability.

The probability of drawing a ten-ruble coin: - Probability = (Number of ten-ruble coins) / (Total number of coins) - Probability = 1 / (8 + 5 + 2 + 1) = 1 / 16

The probability of drawing a five-ruble coin and a two-ruble coin: - Probability = (Number of five-ruble coins) / (Total number of coins) * (Number of two-ruble coins) / (Total number of coins) - Probability = (2 / 16) * (5 / 16) = 10 / 256

The probability of drawing three two-ruble coins: - Probability = (Number of two-ruble coins) / (Total number of coins) * (Number of two-ruble coins - 1) / (Total number of coins - 1) * (Number of two-ruble coins - 2) / (Total number of coins - 2) - Probability = (5 / 16) * (4 / 15) * (3 / 14) = 60 / 3360

Now, we can sum up these probabilities to find the total probability of the remaining sum being at least 36 rubles: - Total Probability = (1 / 16) + (10 / 256) + (60 / 3360) = 0.0625 + 0.0390625 + 0.0178571 ≈ 0.1194

The probability of the remaining sum being at least 36 rubles when drawing a coin at random is approximately 0.1194, or 11.94%.