In a family with 4 children what is the probability of having 1 boy and then 3 girls, in that order? (Exclude multiple births and assume all outcomes are equally likely).
In a family with 4 children, what is the probability of having 1 boy and 3 girls, in any order? (Exclude multiple births and assume all outcomes are equally likely).
your first part is
(1/2)(1/2)(1/2)(1/2)
= (1/2)^4
= 1/16
2nd part:
possible outcomes:
BGGG
GBGG
GGBG
GGGB , so 4 in all
each one has a prob of 1/16
so 4/16 or 1/4
In a family with 3 children what is the probability of having 1 boy and then 2 girls, in that order? (Exclude multiple births and assume all outcomes are equally likely).
In a family with 3 children, what is the probability of having 1 boy and 2 girls, in any order? (Exclude multiple births and assume all outcomes are equally likely).
Oh boy, probability questions! Well, let me put on my clown nose and do some math for you.
For the first question, the probability of having 1 boy and then 3 girls in that specific order is quite straightforward. Since each child has a 50% chance of being a boy and 50% chance of being a girl, the chances of having a specific sequence of 1 boy and then 3 girls is (1/2) * (1/2) * (1/2) * (1/2), which simplifies to 1/16. So the probability is 1 out of 16.
Now, for the second question, where we don't care about the order (because boys and girls are all equally amazing), we need to consider all the possible combinations. The possible combinations of 1 boy and 3 girls are: BGGG, GBGG, GGBG, and GGGB. So, there are 4 different orderings. Since each ordering has a 1/16 chance of occurring, we simply add up the probabilities: 4/16, which simplifies to 1/4. So the probability is 1 out of 4.
I hope my clownish explanation didn't make you too dizzy!
To find the probability of having 1 boy and then 3 girls, in that order, in a family with 4 children, we can use the formula for probability:
P(A) = (Number of favorable outcomes) / (Total number of possible outcomes)
In this case, the total number of possible outcomes is 2^4 = 16, as each child can be either a boy or a girl, and there are 4 children.
The number of favorable outcomes for having 1 boy and then 3 girls in that order is 1, since there is only one specific arrangement that satisfies this condition.
Therefore, the probability of having 1 boy and then 3 girls, in that order, in a family with 4 children is:
P(A) = 1 / 16 = 0.0625 or 6.25%
Now, let's calculate the probability of having 1 boy and 3 girls, in any order.
To do this, we need to find the number of favorable outcomes, which are the different ways we can arrange 1 boy and 3 girls among the 4 children.
The number of favorable outcomes can be calculated using the formula for combinations:
C(n, k) = n! / (k! * (n-k)!)
Where n is the total number of objects and k is the number of objects choosing at a time.
In this case, n = 4 (the total number of children) and k = 1 (the number of boys).
C(4, 1) = 4! / (1! * (4-1)!) = 4! / (1! * 3!) = (4 * 3 * 2 * 1) / (1 * 2 * 1) = 4
So, there are 4 different ways to arrange 1 boy and 3 girls among the 4 children.
Therefore, the probability of having 1 boy and 3 girls, in any order, in a family with 4 children is:
P(A) = 4 / 16 = 0.25 or 25%
To calculate the probability of having 1 boy and 3 girls in a family with 4 children, we need to consider two scenarios: one where the order matters (1 boy followed by 3 girls) and another where the order does not matter (1 boy and 3 girls in any order).
1. Probability of having 1 boy followed by 3 girls in that order:
To calculate this probability, we need to consider the possible outcomes where the first child is a boy and the next three are girls. In this case, we have one favorable outcome (BGGG) out of the total number of possible outcomes for a family with 4 children, which is 2⁴ = 16 (since each child can be either a boy or girl). Therefore, the probability can be calculated as:
Probability = Favorable outcomes / Total outcomes = 1 / 16 = 0.0625 or 6.25%
2. Probability of having 1 boy and 3 girls in any order:
To calculate this probability, we need to consider the possible outcomes where there is exactly one boy and three girls, regardless of the order. In this case, we can have four different favorable outcomes: BGGG, GBGG, GGBG, and GGGB. The total number of possible outcomes for a family with 4 children remains 2⁴ = 16. Therefore, the probability can be calculated as:
Probability = Favorable outcomes / Total outcomes = 4 / 16 = 0.25 or 25%.