It is assume that when she children are born they are like they're equally likely to be boys or girls what is probability that a family of four children contain three boys and two girls
To find the probability of having three boys and two girls in a family of four children, we need to consider the different ways this can occur.
In a family of four children, the possible combinations are:
BBBG
BBGB
BGBB
GBBB
BGGG
GBGG
GGBG
GGGB
So, there are a total of 8 possible combinations.
Out of these 8 combinations, only 1 combination has three boys (B) and two girls (G), which is BBBG.
Therefore, the probability that a family of four children contains three boys and two girls is 1 out of 8, or 1/8.
To determine the probability of a family of four children containing three boys and two girls, we can use the concept of binomial probability.
In this case, we have a binomial distribution with four trials, where the probability of success (having a boy) is 0.5 and the probability of failure (having a girl) is also 0.5.
The probability of getting three boys and two girls can be calculated using the binomial probability formula:
P(X = k) = (n choose k) * p^k * (1-p)^(n-k)
where:
- P(X = k) is the probability of getting k successes (boys),
- n is the total number of trials (number of children),
- k is the number of successes (number of boys),
- p is the probability of success (probability of having a boy).
In this case, n = 4, k = 3, and p = 0.5. Substituting these values into the formula:
P(X = 3) = (4 choose 3) * 0.5^3 * (1-0.5)^(4-3)
Calculating the values:
P(X = 3) = (4 choose 3) * 0.5^3 * 0.5^1
= 4 * 0.125 * 0.5
= 0.25
Therefore, the probability that a family of four children contains three boys and two girls is 0.25 or 25%.
To calculate the probability of a family having three boys and two girls, we can use the concept of combinations. The probability of having a boy (B) or a girl (G) is considered to be 1/2 (assuming an equal likelihood of each gender).
Now, let's break down the possible combinations of three boys (BBB) and two girls (GG) in a family of four children:
1. Boy-Boy-Boy-Girl: (BBBG)
2. Boy-Boy-Girl-Boy: (BBGB)
3. Boy-Girl-Boy-Boy: (BGBB)
4. Girl-Boy-Boy-Boy: (GBBB)
5. Boy-Boy-Girl-Girl: (BBGG)
6. Boy-Girl-Boy-Girl: (BGBG)
7. Girl-Boy-Boy-Girl: (GBBG)
8. Boy-Girl-Girl-Boy: (BGGB)
9. Girl-Boy-Girl-Boy: (GBGB)
10. Girl-Girl-Boy-Boy: (GGBB)
There are a total of 10 possible combinations, and we are interested in the three boys and two girls combination (BBBGG). Since each combination has an equal probability of occurring (1/2^4), we can calculate the probability by dividing the number of favorable outcomes (1) by the total number of outcomes (10):
Probability of having three boys and two girls:
P(BBBGG) = 1/10
Therefore, the probability of a family of four children containing three boys and two girls is 1/10 or 0.1 (10%).