Question

В результате обследования были выделены семьи, имеющие по четыре ребёнка. Считая вероятности появления мальчика в семье равной (0,7), определить вероятности появлений в ней: а) одного мальчика; б) двух мальчиков.

Answer 1

Ответ:

Решение: Используем формулу Бернулли: Р" = С"" p"q""

В данной задаче: n = 4 - всего детей в семье; m - количество мальчиков в семье. p = 0.5 - вероятность рождения мальчика:

q =1 - p =1- 0.5 = 0.5 - вероятность рождения девочки; Р." - вероят вероятность того, что среди 4-х детей будет ровно т мальчиков.

a) Р = C1(0,5)(0,5)3 = 4 (0,5)* = 0,25 - вероятность того, что среди 4-х детей

будет один мальчик

Answer 2

Probability of Having a Boy in a Family

To determine the probabilities of having one boy or two boys in a family with four children, we can use the concept of binomial distribution. The probability of having a boy in a family is given as 0.7.

Probability of Having One Boy

The probability of having exactly one boy in a family of four children can be calculated using the binomial probability formula: P(X=k) = (n choose k) * (p^k) * ((1-p)^(n-k)) Where: - n = total number of children (4 in this case) - k = number of boys we want to find the probability for (1 in this case) - p = probability of having a boy (0.7 in this case)

Plugging in the values: P(X=1) = (4 choose 1) * (0.7^1) * ((1-0.7)^(4-1))

Calculating the value: P(X=1) = (4 choose 1) * (0.7^1) * (0.3^3)

Probability of Having Two Boys

Similarly, the probability of having exactly two boys in a family of four children can be calculated using the same formula: P(X=k) = (n choose k) * (p^k) * ((1-p)^(n-k)) Where: - n = total number of children (4 in this case) - k = number of boys we want to find the probability for (2 in this case) - p = probability of having a boy (0.7 in this case)

Plugging in the values: P(X=2) = (4 choose 2) * (0.7^2) * ((1-0.7)^(4-2))

Calculating the value: P(X=2) = (4 choose 2) * (0.7^2) * (0.3^2)

Conclusion

By calculating the above probabilities, we can determine the likelihood of having one boy or two boys in a family with four children, given the probability of having a boy is 0.7.