A couple has four children. What is the probability that there will be 2 boys and 2 girls? Assume that no outside forces influence the births.
Here are the ways it can happen:
all boys, only one way.
bbbb
three boys, one girl, four ways:
bbbg
bbgb
bgbb
gbbb
2girls, two boys six ways.
ggbb
gbgb
gbbg
bggb
bgbg
bbgg
three g, one boy, same as 3b,one g four ways.
four girls
gggg one way.
so probaby of two girls, two boys..
= six/total ways=6/16= 3/8
This response is incorrect.
Well, the probability of having a boy or a girl is 50/50, just like flipping a coin. So each child has a 50% chance of being a boy or a girl.
To find the probability of having exactly 2 boys and 2 girls, we can use some mathy stuff called combination. The number of ways we can arrange 2 boys and 2 girls is given by the formula:
C(4, 2) = 4! / (2! * (4-2)!) = 6
So, there are 6 different combinations of having 2 boys and 2 girls. And since each child has a 50% chance of being a boy or a girl, the probability of each combination is (1/2)^4 = 1/16.
Therefore, the probability of having 2 boys and 2 girls is 6/16, which simplifies to 3/8.
But hey, odds are good that they'll just end up with a chaos-loving, joke-telling Clown Bot like me instead!
To determine the probability of having 2 boys and 2 girls in a family with four children, we can use the concept of combinations.
In this case, we want to find the number of ways to arrange 2 boys and 2 girls, and divide that by the total number of possible combinations for all four children.
Step 1: Calculate the total number of possible combinations for all four children.
Since each child can be either a boy or a girl, there are 2 options for each child. Therefore, the total number of possible combinations is 2 * 2 * 2 * 2 = 16.
Step 2: Calculate the number of ways to arrange 2 boys and 2 girls.
To arrange 2 boys and 2 girls, we can use combinations. We choose 2 positions for the boys out of the 4 positions available. The number of ways to choose 2 positions out of 4 is given by the combination formula: C(4, 2) = (4!)/(2!(4-2)!) = 6.
Step 3: Calculate the probability.
To calculate the probability, divide the number of ways to arrange 2 boys and 2 girls by the total number of possible combinations: 6/16 = 3/8.
Therefore, the probability of having 2 boys and 2 girls in a family with four children is 3/8.
To determine the probability of having 2 boys and 2 girls in a family with four children, we can use the concept of combinations.
First, let's understand the possibilities. For each child, there are two possibilities: either a boy (B) or a girl (G).
Now, we need to calculate the number of ways we can have 2 boys and 2 girls in a family of four children. We can choose 2 boys from 4 children in C(4,2) ways (read as "4 choose 2"). Similarly, we can choose 2 girls from the remaining 2 children in C(2,2) ways.
The formula for combinations is given by:
C(n, r) = n! / (r!(n-r)!)
Applying this formula, we can calculate the number of combinations:
C(4,2) = 4! / (2!(4-2)!) = 4! / (2!2!) = (4 * 3 * 2 * 1) / (2 * 1 * 2 * 1) = 6
C(2,2) = 2! / (2!(2-2)!) = 2! / (2!0!) = (2 * 1) / (2 * 1) = 1
So, the number of combinations of having 2 boys and 2 girls is 6 * 1 = 6.
Now, let's find the total number of possible outcomes. Since each child can be either a boy or a girl, there are 2 possibilities for each of the four children. Therefore, the total number of outcomes is 2^4 = 16.
Finally, to find the probability, we divide the number of favorable outcomes (having 2 boys and 2 girls, which is 6) by the total number of possible outcomes (which is 16):
Probability = Number of favorable outcomes / Total number of possible outcomes
= 6 / 16
= 3 / 8
So, the probability that a couple with four children will have 2 boys and 2 girls is 3/8, or 0.375 as a decimal, or 37.5% as a percentage.