Mathematics, 15.07.2019 10:50 trippsmom0671

Find the probability of getting exactly 6 girls in 8 births.

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Answer from: lzrd3rik

The probability of getting exactly 6 girls in 8 births is 0.1093

Step-by-step explanation:

Given : 6 girls in 8 births.

To find : The probability of getting exactly 6 girls in 8 births.

Solution :

The probability of getting girl is $\frac{1}{2}$

The probability of getting 6 girl is $(\frac{1}{2})^6$

Since we have 6 girls,

We also need to find the probability of getting 2 boys, which is

$(\frac{1}{2})^2$

There are ^8C_6 ways to get 6 girls in 8 births

i.e, $^8C_6=\frac{8!}{6!\times 2!}$

$^8C_6=\frac{8\times 7\times 6!}{6!\times 2\times 1}$

^8C_6=28

There are 28 ways to get 6 girls in 8 births.

The probability of getting exactly 6 girls in 8 births.

$=28\times (\frac{1}{2})^6\times (\frac{1}{2})^2$

$=28\times 0.015625\times 0.25$

=0.109375

Therefore, The probability of getting exactly 6 girls in 8 births is 0.1093

Answer from: originnjoku3632

The probability of having exactly girls in birth is $\boxed{\bf 0.10937}$ .

Further explanation:

Concept used:

The probability of an event is calculated as follows:

$\boxed{P(E)=\dfrac{n(E)}{n(S)}}$

Here, n(E) is the number of favorable outcomes in an event and n(S) is the number of element in sample space .

The probability of exactly success in trial is expressed as follows:

$\boxed{P(F)=^{n}C_{r}p^{r}q^{n-r}}$

Here, is the probability of success in an event and is the probability of failure.

Calculation:

Consider as an event of having a girl in first birth and P(A) as the probability of event .

The probability of having a girl is $P(A)=\frac{1}{2}$ .

Assume that is the complement event of an event and P(A') is the probability of complementary event .

The event is the event of not having a girl in the first birth.

The probability of event is calculated as follows:

$\boxed{P(A')=1-P(A)}$ …… (1)

Substitute $P(A)=\frac{1}{2}$ in the equation (1) to obtain the probability of event .

$\begin{aligned}P(A')&=1-\dfrac{1}{2}\\&=\dfrac{1}{2}\end{aligned}$

The probability of having exactly girls in birth is calculated as follows:

$\begin{aligned}P(F&)=^{8}C_{6}\left(\dfrac{1}{2}\right)^{6}\left(\dfrac{1}{2}\right)^{8-6}\\&=\dfrac{8!}{6!\cdot 2!}\cdot (0.5)^{6}\cdot (0.5)^{2}\\&=28(0.5)^{8}\\&=0.10937\end{aligned}$

Thus, the probability of having exactly girls in birth is $\boxed{\bf 0.10937}$ .

Learn more:

1. Learn more about problem on numbers:

2. Learn more about problem on function

Answer details:

Grade: Senior school

Subject: Mathematics

Chapter: Probability

Keywords: Probability, exact event, sample space, number of element, complement event, success, failure, favorable, trial, P(E)=n(E)/n(S), P(A')=1-P(A).

Answer from: Quest

black/brown

step-by-step explanation:

well, you see here, jamal was born to 2 parents, his mother who he lives with and his father who left at a young age and who happens to be younger than him. he stole cookies because he has to steal food due to the fact that he spends his government poverty checks on pot and women.

Answer from: Quest

step-by-step explanation:

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