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There are three family consisting of 3 boys 2girls, 2 boys and 2 girls, 2boys and 3 girls. a family is selected at random and from ut two children are selected. what is the probability that both of them are girls?
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There are three family consisting of 3 boys 2girls, 2 boys and 2 girls...
Given Information:
- Family 1: 3 boys and 2 girls
- Family 2: 2 boys and 2 girls
- Family 3: 2 boys and 3 girls
- One family is selected randomly
- Two children are selected from the family
Probability of Selecting a Family:
The probability of selecting each family is:
- Family 1: 1/3
- Family 2: 1/3
- Family 3: 1/3
Probability of Selecting Two Girls:
We need to calculate the probability of selecting two girls from the chosen family. We can use the following formula:
P(two girls) = P(F1) * P(2 girls from F1) + P(F2) * P(2 girls from F2) + P(F3) * P(2 girls from F3)
Family 1:
The probability of selecting two girls from Family 1 is:
P(2 girls from F1) = (2/5) * (1/4) = 1/10
Family 2:
The probability of selecting two girls from Family 2 is:
P(2 girls from F2) = (2/4) * (1/3) = 1/6
Family 3:
The probability of selecting two girls from Family 3 is:
P(2 girls from F3) = (3/5) * (2/4) = 3/10
Total Probability:
Now we can substitute the above probabilities into our formula:
P(two girls) = (1/3) * (1/10) + (1/3) * (1/6) + (1/3) * (3/10) = 11/60
Final Answer:
The probability of selecting two girls from a family selected randomly is 11/60.
Explanation:
The given information provides the number of boys and girls in each family. We need to calculate the probability of selecting two girls from a family chosen randomly. To do this, we first calculate the probability of selecting each family. Then, we calculate the probability of selecting two girls from each family using the given gender distribution. Finally, we use the formula to calculate the total probability of selecting two girls from a family chosen randomly. The final answer is 11/60.
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There are three family consisting of 3 boys 2girls, 2 boys and 2 girls, 2boys and 3 girls. a family is selected at random and from ut two children are selected. what is the probability that both of them are girls?
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