Q.3. Compute the probability that: (a) their sum is odd; (b) their product is even. Three distinct integers are chosen at random from the first 15 positive integers.

A gender-selection technique is designed to increase the likelihood thata baby will be a girl. In the results of the gender-selection technique, 912 birfhs consisted of 462 baby girls and 450 baby boys. In analyzing these results, assume that boys and girls are equally likely a. Find the probability of getting exactly 462 girls in 912 births. b. Find the probability of getting 462 or more girls in 912 births. If boys and girls are equally likely, is 462 girls in 912 births unusually high? J inb rAbabilitiocalaunt forninate Eertho denbnini in cEontin ha coouk romnodLa n arna H frono ert /h1 a. The probability of getting exactly 462 girls in 912 births is (Round to four decimal places as needed.) Enter your answer in the answer box and then click Check Answer. Check Ansuer parts remaining Clear All P Pearson 9:50 PM 11/29/2019 O e ch

12. The table shows the number of students who took the March Bar Test for the first time and thc numbcr of students who repact the exam. Passed Failed Total 6458 2058 First time 4427 2252 1845 407 Repeat Total 8737 4834 3903 a. )Find the probability that a student failed, given that the student took the exam for the first time. b.) Find the probability that a studnt repeated the exam, given the student passed.

B positive: 24 B negative: 6 hat is the probability that a rand 0 Has Type O blood? ) Is Rh-negative? Has Type O blood and is Rh-ne | Has Type O blood or is Rh-neg Has Type O blood, given that t Is Rh-negative, given that they

You randomly select an integer from 0 to 7 (inclusively) and then randomly select an integer from U to 4 (inclusively). What is the probability of selecting a 2 both times? The probability is. (Type an integer or a decimal. Do not round.)

of Suppose a child is born to two parents who are cystic fibrosis carriers. Construct a chart of gene combinations to find the probability that the child will neither have nor carry the disease. P(neither have nor carry the disease) = (Type an integer or a simplified fraction.) of of y of of C Time Remaining: 01-0637

Computers A and B can independently generate positive integers: • Computer A generates positive integer n with probability a/3", where a is a constant. • Computer B generates positive integer n with probability 3/n!, where ß is a constant. (a) Find the probability that the number generated by A is larger than the number generated by B. (b) Find the probability that the number generated by A is smaller than the number generated by B.

Zou and Chou are practicing their 100-meter sprints by running 6 races against each other. Zou wins the first race, and after that, 1 the probability that one of them wins a race is , if they won the previous race but only , if they lost the previous race. The 3 3 m probability that Zou will win exactly 5 of the 6 races is -, where m and n are relatively prime positive integers. Find m + n. n

Consider 10 independent tosses of a biased coin with the probability of Heads at each toss equal to p, where 0 < p < 1. (a) Let A be the event that there are exactly 6 Heads in the first 8 tosses. Let B be the event that the 9th toss results in Heads. Find P(B | A) and express it in terms of p. (b) Find the probability that there are exactly 3 Heads in the first 4 tosses and exactly 2 Heads in the last 3 tosses. Express your answer in terms of p. (c) Given that there were exactly 4 Heads in the first 7 tosses, find the probability that the 2nd Heads occurred at the 4th toss. Give a numerical answer. (d) Find the probability that there are exactly 5 Heads in the first 8 tosses and exactly 3 Heads in the last 5 tosses.

2:51 A flush in the card game of poker occurs if a player gets five cards that are all the same suit (clubs, diamonds, hearts, or spades). Complete parts (a) and (b) to obtain the probability of being dealt a flush in five cards. (a) Initially concentrate on one suit, say clubs. There are 13 clubs in a deck. Compute P(five clubs) = P(first card is clubs and second card is clubs and third card is clubs and fourth card is clubs and fifth card is clubs). P(five clubs) = 0.000495 (Round to six decimal places as needed.) (b) A flush can occur if a player receives five clubs or five diamonds or five hearts or five spades. Compute P(five clubs or five diamonds or five hearts or five spades). Note that the events are mutually exclusive. P(five clubs or five diamonds or five hearts or five spades) = (Round to three decimal places as needed.) Vo) 1 LTE 4G 1% ||| = O