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Children's genders are not independent and therefore there is no simple answer.

However, if you do assume that their genders are independent then the probability is 1/3.

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Q: A woman is chosen at random among all woman who have two children She is asked if she has at least one son and says yes. What is the probability of here other child being a boy?
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What is the probability tossing a fair coin n times?

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What is the probability of at least one birthday match among a group of 41 people?

The probability of at least 1 match is equivalent to 1 minus the probability of there being no matches. The first person's birthday can fall on any day without a match, so the probability of no matches in a group of 1 is 365/365 = 1. The second person's birthday must also fall on a free day, the probability of which is 364/365 The probability of the third person also falling on a free day is 363/365, which we must multiply by the probability of the second person's birthday being free as this must also happen. So for a group of 3 the probability of no clashes is (363*364)/(365*365). Continuing this way, the probability of no matches in a group of 41 is (365*364*363*...326*325)/36541 This can also be written 365!/(324!*36541) Which comes to 0.09685... Therefore the probability of at least one match is 1 - 0.09685 = 0.9032 So the probability of at least one match is roughly 90%


Only 7.2 percent of the population has O-negative blood A mobile blood center is visited by 20 donors in afternoon Let X denote number of universal donors among them probability that X is at least 2?

The probability that any given donor is a universal donor is 0.072.We need the probability that the number of universal donors in this group of 20 is not zero or one.Probability of getting zero universal donors: ( 1 - 0.072 )^20 = 0.224367Probability of getting one such donor: 0.348156 (given by the binomial probability density function: probability of one success in 20 trials with p=0.072)Total: 0.224367 + 0.348156 = 0.572523, the probability of zero or one donorsBut we want 1 - 0.572523 = 0.427477, the probability of getting two or more such donors.^ stands for 'to the power of'


Among the contestants in a competition are 49 women and 29 men so if 5 winners are randomly selected what is the probability that they are all men?

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One letter is randomly selected from the word math and a second letter is randomly selected from the word jokes what is the probability that both letters are vowels?

Word 1) 'math' has one vowel letter among a total of 4 letters. The probability of randomly selecting the vowel letter 'a' is P(v) = 1/4. Word 2) 'jokes' has two vowel letters among a total of 5 letters. The probability of randomly selecting a vowel letter is P(v) = 2/5. The probability of randomly selecting a vowel letter from the first word and a vowel letter from the second word is: P(v1,v2) = 1/4 (2/5) = 2/20 = 1/10 = 0.10 = 10.0%

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