Question

In a certain? country, the true probability of a baby being a boy is 0.534. among the next six randomly selected births in the? country, what is the probability that at least one of them is a girl??

Answer 1

Finding the "probability that at least one is girl" can be done much easier by subtracting the "probability that none is girl" from 1, since these 2 events are the complement of each other, and either one or the other, but never both, may happen.

consider the tree diagram of the problem, check the picture, each branching represents a birth. The only branch where there is no girl (no g), is 

bbbbbb with a probability of (1-0.534=0.466) per each letter b. 

we know that the probability of a particular branch is the multiplication of the probabilities of each letter in the branch.

so in the case, P(bbbbbb)=$(0.466)^{6}= 0.01$

finally, P(at least 1 girl) = 1- P(no girl)=1-P(bbbbbb)=1-0.01=0.99


Answer: 0.99

Answer 2

The probability that at least one of them is a girl is about 0.977

Further explanation

The probability of an event is defined as the possibility of an event occurring against sample space.

$\large { \boxed {P(A) = \frac{\text{Number of Favorable Outcomes to A}}{\text {Total Number of Outcomes}} } }$

Permutation ( Arrangement )

Permutation is the number of ways to arrange objects.

$\large {\boxed {^nP_r = \frac{n!}{(n - r)!} } }$

Combination ( Selection )

Combination is the number of ways to select objects.

$\large {\boxed {^nC_r = \frac{n!}{r! (n - r)!} } }$

Let us tackle the problem.

This problem is about Probability.

Given:

The true probability of a baby being a boy P(B) = 0.534

The true probability that all of six randomly selected births in the country are boys is :

$P(6B) = P(B) \times P(B) \times P(B) \times P(B) \times P(B) \times P(B)$

$P(6B) = \boxed {(P(B))^6}$

The true probability that at least one of them is a girl is:

$P(G\geq 1) = 1 - P(6B)$

$P(G\geq 1) = 1 - (P(B))^6$

$P(G\geq 1) = 1 - (0.534)^6$

$P(G\geq 1) \approx \boxed {0.977}$

Learn more

• Different Birthdays : brainly.com/question/7567074
• Dependent or Independent Events : brainly.com/question/12029535
• Mutually exclusive : brainly.com/question/3464581

Answer details

Grade: High School

Subject: Mathematics

Chapter: Probability

Keywords: Probability , Sample , Space , Six , Dice , Die , Binomial , Distribution , Mean , Variance , Standard Deviation