Mathematics: Sandra needs to buy meters of chain for a home project. which decimal number is equal to the fraction ? 8.4 8.04 0.84 0.804 need asap

Sandra needs to buy meters of chain for a home project.

Ответ:

ynclankaedon

12.12.2021

50% probability of a couple having a baby boyboy when their sixth child is born, given that the first five were all boys.

Step-by-step explanation:

For each child, there are only two possible outcomes. Either it is a boy, or it is a girl. The probability of a child being a boy or a girl is independent of the other children. So we use the binomial probability distribution to solve this question.

The conditional probability formula is also used.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

Conditional Probability

We use the conditional probability formula to solve this question. It is

$P(B|A) = \frac{P(A \cap B)}{P(A)}$

In which

P(B|A) is the probability of event B happening, given that A happened.

$P(A \cap B)$ is the probability of both A and B happening.

P(A) is the probability of A happening.

Find the probability of a couple having a baby boyboy when their sixth child is born, given that the first five children were all boys.

Event A: First five children being boys.

Event B: Sixth children being a boy.

P(A):

First five children being boys.

P(X = 5) when n = 5.

Equally likely to be boy or girl, so p = 0.5.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(A) = P(X = 5) = C_{5,5}.(0.5)^{5}.(0.5)^{0} = 0.03125$

Intersection:

Intersection between the first five children being boys and the sixth also being a boy, so P(X = 6) when n = 6.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(A \cap B) = P(X = 6) = C_{6,6}.(0.5)^{6}.(0.5)^{0} = 0.015625$

Probability:

$P(B|A) = \frac{0.015625}{0.03125} = 0.5$

50% probability of a couple having a baby boyboy when their sixth child is born, given that the first five were all boys.

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Sandra needs to buy meters of chain for a home project. which decimal number is equal to the fraction ? 8.4 8.04 0.84 0.804 need asap

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