STAT Probability

disjoint

cannot occur at the same time, so given P(A) = 0.30 and P(B) = 0.60, then P(A and B) = 0 because disjoint means cannot occur at the same time. Both are independent.

40% male, what is the probability that they are the same gender

0.40*0.40+0.60*0.60 = 0.52

8% of the male have kidney stone, select two males, let x = first male have kidney stone, let y = second male had kidney stone, what is true?

X and Y are independent

Let A and B be two independent events. If P(A) = 0.4 what can you say about P (A|B)?

it is equal to 0.4 P(A and B) = P(A) * P(B) conditional probability= P(A and B) /P(B)

What is the probability that when a theft occurs, none of four systems will detect it? Given, fail to detect = 0.01

(0.01)^4

According to the information that comes with a certain prescription drug, when taking this drug, there is a 20% chance of experiencing nausea (N) and a 50% chance of experiencing decreased sexual drive (D). The information also states that there is a 15% chance of experiencing both side effects. What is the probability of experiencing nausea or a decrease in sexual drive? (a) .10 (b) .40 (c) .55 (d) .70 (e) .85 What is the probability of experiencing exactly one of the two side effects? (A probability table could be useful.) (a) .10 (b) .40 (c) .55 (d) .70 (e) .85 What is the probability of experiencing neither of the side effects? (a) .10 (b) .40 (c) .45 (d) .70 (e) .85

(c) .55 (d) .70 (c) .45

These days with the cost of a college education it is important to be able to graduate with a bachelors degree in 4 years. The National Association of Independent Colleges and Universities (NAICU) certainly would encourage students to attend independent schools. They provided the following information: (i) 20% of all college students attend private colleges and universities. (ii) 55% of all college students graduate in 4 years. (iii) 79% of students attending private colleges and universities graduate in 4 years. What is the probability that a randomly chosen student attended a private school and graduated in 4 years?

.20 / .79 = .2532

In a random sample of 100 college students, 60 were females, 65 were under 21 yrs of age, and 15 males were 21 yrs of age or older. A student is selected at random from this sample. What is the probability that a female student of age 21 or older is selected? 0.20 0.21 0.75 0.95

0.20

Two methods, A and B, are available for teaching a certain industrial skill. There is an 80% chance of successfully learning the skill if method A is used, and a 95% chance of success if method B is used. However, method B is substantially more expensive and is therefore used only 25% of the time (method A is used the other 75% of the time). The following notations are suggested: A—method A is used B—method B is used L—the skill was Learned successfully

P(A) = .75, P(B) = .25, P(L | A) = .80, P(L | B) = .95

Again here is the information about the characteristics of a basketball team's season: 60% of all the games were at-home games. Denote this by H (the remaining were away games). 25% of all games were wins. Denote this by W (the remaining were losses). 20% of all games were at-home wins. If the team won a game, how likely is it that this was a home game?

P(H|W) = 0.20/0.25=0.80 P(H|W) = P(W and H)/P(W) P(W) = 0.25 P(Home wins) = 0.20

Again we have two methods, A and B, available for teaching a certain industrial skill. There is an 80% chance of successfully learning the skill if method A is used, and a 95% chance of success if method B is used. However, method B is substantially more expensive and is therefore used only 25% of the time (method A is used the other 75% of the time). What is the probability that a randomly chosen worker will learn the skill successfully?

P(L) = .75 * .80 + .25 * .95 = .8375

he first three questions refer to the following information: Suppose a basketball team had a season of games with the following characteristics: 60% of all the games were at-home games. Denote this by H (the remaining were away games). 25% of all games were wins. Denote this by W (the remaining were losses). 20% of all games were at-home wins. Question 1 of 5 Points: 10 Of the at-home games, we are interested in finding what proportion were wins. In order to figure this out, we need to find:

P(W | H)

Dogs are inbred for such desirable characteristics as blue eye color; but an unfortunate by-product of such inbreeding can be the emergence of characteristics such as deafness. A 1992 study of Dalmatians (by Strain and others, as reported in The Dalmatians Dilemma) found the following: (i) 31% of all Dalmatians have blue eyes. (ii) 38% of all Dalmatians are deaf. (iii) 42% of blue-eyed Dalmatians are deaf. Based on the results of this study is "having blue eyes" independent of "being deaf"?

P(blue eyes and deaf) does not equal P(deaf | blue eyes) But P(blue eyes and deaf) = P(blue eyes) * P (deaf) if they are independent If knowing a Dalmation has blue eyes doesn't change the probability that it is deaf. P(deaf|blue eyes) = P(deaf) So No, since 0.38 is not equal to 0.42

A person at a carnival decides to toss rings until he hits the target, but he will not toss more than 3 times. Let H denote a hit and M denote a miss. What is the sample space for this random experiment? S = {HHH, HHM, HMH, HMM, MHH, MHM, MMH, MMM} S = {H, HH, HHH} S = {H, HM, HHM, HHH} S = {H, MH, MMH} S = {H, MH, MMH, MMM}

S = {H, MH, MMH, MMM}

Again we have two methods, A and B, available for teaching a certain industrial skill. There is an 80% chance of successfully learning the skill if method A is used, and a 95% chance of success if method B is used. However, method B is substantially more expensive and is therefore used only 25% of the time (method A is used the other 75% of the time). A worker learned the skill successfully. What is the probability that he was taught by method A?

The quotient of (.75 * .80) and (.75 * .80 + .25 * .95) which is approximately equal to .7164.

In a random sample of 60 middle school students the following data were collected. If a male student is selected at random from this sample, what is the probability that he is a sixth grader. a. 12/25 b. 12/30 c. 12/60 d. 25/60

answer use 30 male not 60 male and women ans: 12/30

Again here is the information about the characteristics of a basketball team's season: 60% of all the games were at-home games. Denote this by H (the remaining were away games). 25% of all games were wins. Denote this by W (the remaining were losses). 20% of all games were at-home wins. Of the at-home games, what proportion of games were wins?

correct Ans: P(H) = 0.60 P(W | H) = P(H and W)/P(H)= 0.33 0.20/0.60 my mistake: P(H and W) = 0.20

A person at a carnival decides to toss rings at a target 3 times. Let H denote a hit and M denote a miss. Define the event A as "the person hits the target at least one time." What are the possible outcomes for this event? {H, HH, HHH} {H, MH, MMH} {HHH, HHM, HMH, HMM, MHH, MHM, MMH} {HHH, HHM, HMH, HMM, MHH, MHM, MMH, MMM} {HMM, MHM, MMH}

{HHH, HHM, HMH, HMM, MHH, MHM, MMH, MMM}