in a family with two children, what are the probabilities of two boys, the first is a girl the second is a boy, neither is a girl, at least one girl, assuming that the birth of boys and girls is equally likely.
The different possibilities are:
bb
bg
gb
gg
From this, you can figure out how many of the four possibilities fit. (Having two boys is the same as having no girls.)
I hope this helps.
in a family with two children, what are the probabilities of two boys, the first is a girl the second is a boy, neither is a girl, at least one girl, assuming that the birth of boys and girls is equally likely.
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To calculate the probabilities in this scenario, we need to consider the possible outcomes and determine the probability of each.
1. Two boys: In a family with two children, the probability of having two boys is 1/4, as there are four equally likely outcomes: BB, BG, GB, and GG (where B represents a boy and G represents a girl). Since we only want the probability of two boys, we focus on the BB outcome.
2. The first is a girl, the second is a boy: To calculate this probability, we need to consider the outcomes where the first child is a girl (G). The possible outcomes are BG and GG. Therefore, the probability of the first child being a girl and the second child being a boy is 2/4 or 1/2.
3. Neither is a girl: This scenario includes the outcome BB (two boys only). Therefore, the probability is 1/4.
4. At least one girl: To calculate this probability, we need to consider the outcomes where at least one child is a girl. These outcomes are BG, GB, and GG. Therefore, the probability of having at least one girl is 3/4.
In summary:
- Probability of two boys: 1/4
- Probability of first is a girl, second is a boy: 1/2
- Probability of neither is a girl: 1/4
- Probability of at least one girl: 3/4
To determine the probabilities in this scenario, we can use basic principles of probability. Let's break down each case:
1. Two boys: In a family with two children, the probability of having two boys is 1/2 * 1/2 = 1/4 or 25%. The probability of having a boy in the first child is 1/2, and the probability of having a boy in the second child is also 1/2. Since these events are independent, we can multiply the probabilities together to find the combined probability.
2. The first child is a girl, the second child is a boy: In this case, we have two possibilities - the first child can be a girl and the second child can be a boy (GB) or the first child can be a boy and the second child can also be a boy (BB). Since the probability of having a girl or a boy is equal (1/2), the probability of having GB is 1/2 * 1/2 = 1/4 or 25%. Similarly, the probability of having BB is also 1/4 or 25%. Therefore, the probability of the first child being a girl and the second child being a boy is 1/4 + 1/4 = 1/2 or 50%.
3. Neither is a girl: In this case, we have only one possibility, which is BB. Therefore, the probability of neither child being a girl is 1/4 or 25%.
4. At least one girl: This case includes all possibilities where at least one child is a girl. Here we have three possibilities - GB, BG, and GG. The probability of GB, as discussed earlier, is 1/4 or 25%. Similarly, the probability of BG is also 1/4 or 25%. The probability of GG is 1/2 * 1/2 = 1/4 or 25%. Therefore, the probability of having at least one girl is 1/4 + 1/4 + 1/4 = 3/4 or 75%.
To summarize:
- Probability of two boys: 25%
- Probability of the first child being a girl and the second child being a boy: 50%
- Probability of neither child being a girl: 25%
- Probability of at least one girl: 75%