1. Suppose that each child born to a couple is equally likely to be a boy...
1. Suppose that each child born to a couple is equally likely to be a boy or a girl, inde- having 5 children, compute the probabilities of the following events: (a) All children are of the same gender (b) The 3 eldest are boys and the others girls. (c) Exactly 3 are boys. (d) The 2 oldest are girls. (e) There is at least 1 girl. 3. In a bolt factory machines A, B, C manifacture, respectively 25, 35 and...
Find the probability of a couple having a baby boy when their fifth child is born, given that the first four children were all boys. Assume boys and girls are equally like Is the result the same as the probability of getting all boys among five children? The probability is _______ (Type an integer or a simplified fraction.) Is this result the same as the probability of getting all boys among five children? A. Yes. The events are all independent. B. Yes. The final...
Consider a couple who gave birth to 4 children (assume a boy is equally likely as a girl) The events space for the experiment S={GGGG,GGGB,GGBG,GGBB,GBGG,GBGB.GBBG GBBB,BGGG BGGB,BGBG,BGBB,BBGG,BBGB,BBBG BBBB } Find the probability of the event E1 of no more than 2 girls in the family () Find the probability of event E2 of no less than two boys in the family (i) (ii) Find the probability of E1 n E2 E1 U E2 (iv) Find the probability of Number Number...
Jane has three children, each of which is equally likely to be a boy or a girl independently of the others. Define the events: A- {all the children are of the same sex}, B- {there is at most one boy;, Cthe family includes a boy and a girl (a) Show that A is independent of B, and B is independent of C (b) Is A independent of C? (c) Do these results hold if Jane has four children?
Discrete Math: A couple is planning to have a family. Let us assume that the probability of having a girl is 0.48 and a boy is 0.52, and that the gender of this couple's children are pairwise independent. They want to have at least one girl and at least one boy. At the same time, they know that raising too many kids is difficult. So here's what they plan to do: they'll keep trying to have children until they have...
Consider a family with eight children. Assuming that the sex each child is determined independently of the others and that each child is equally likely to be female or male, a. What is the probability that exactly four children are female? Hint: Use the binomial distribution. (10 points) b. What is the probability that at most seven children are female? Hint: What is the complement of this event? (10 points)c. Find the conditional probability that the first two children born are female...
In-class worksheet - Binomial distribution Date: 1. Which of the following situations describe a Binomial random variable? (a) Let X be the number of tosses of a fair coin until you obtain a head. (b) The probability of a girl having black hair is 0.6. There are 6 girls altogether. Let X be the number of girls out of the 6 who have black hair. (c) Among 6 girls, there are two with black hair. You pick 4 girls at...
TABLE II. Probability of Independent Events Occurring COMBINATIONS OBSERVED % EXPECTED OBSERVED 1% EXPECTED % 27500 DEVIATION Heads-Heads 1754 10 25 60000 Heads-Tails or Tails-Heads 20 50 + 4 16000 Tails-Tails o 600/0 22.560 100% 10 40 25 100% -1 o 5000 Total 1000 PART III: Probability and Mendelian Genetics we can use the probability to predict the probability of given genetic traits appearing in the offspring of particular parents. Punnett squares can also be used to obtain these results....