1.02 Quiz: Binomial Settings and Binomial Probabilities

What's the probability of getting 1 or 3 fives on 10 rolls of a fair number cube? Hint: Remember the rule for finding P(A or B).

B(10, 1/6, 1) + B(10, 1/6, 3)

Fred is a weightlifter who can lift 800 pounds on 45% of his attempts. Which of these expressions represents the probability Fred will make 30 lifts out of 60?

B(60, .45, 30) - A binomial distribution is written as B(n, p), where n is the number of trials and p is the probability of success for each trial. A specific probability is written as B(n, p, X), where X is the number of successes.

Clarice can shoot free throws with 70% accuracy (she makes 70% of her shots). If she attempts 25 free throws, what's the probability she'll make fewer than 14?

P(x < 14) - P(x < 14) is the sum of the probabilities from 13 down to 0.

What's the probability of getting exactly 1 five when we roll a fair number cube 10 times?

(1 over 10)(1/6)^1(1 - 1/6)^10-1 = binompdf(10, 1/6, 1) = .323 - The number of trials is 10, the probability of success (getting a five) on each trial is 1/6, and you're interested in the probability of getting 1 success. So you want to solve B(10, 1/6, 1), which is .323.

There are 500 cars in Frank's junkyard; 350 blue and 150 red. If Joe randomly selects 25 cars from his yard, what's the probability he'll get from 14 to 20 blue cars, inclusive? Could this be considered an almost binomial event? Choose the best answer.

(25 over 14) (.7)^14(.3)^11 + (25 over 15)(.7)^15(.3)^10 + ... + (25 over 19) (.7)^19(.3)^6 + (25 over 20) (.7)^20(.3)^5 - You want P(14 ≤ x ≤ 20), and this expression adds all of the probabilities from x = 14 to x = 20. It's an almost binomial event because the population is at least 20 times the sample size.

Suppose you roll a six-sided number cube 10 times. What's the probability of getting three fives in those 10 rolls?

.155

If you roll a six-sided number cube 10 times, what's P(x > 3)?

1-binomcdf(10,1/6,3)

Which of the following situations satisfies all the conditions of a binomial setting? (These conditions are: we know the number of repetitions, the outcome of each trial can be considered either a success or a failure, we know the probability of success or failure of any trial, and the probability doesn't change from trial to trial.)

A jar contains 500 balls (300 red and 200 white). Ten balls are randomly selected from the jar, and the number X of red balls is recorded. - This is an almost binomial situation. The probability of success is slightly different for each trial because each time you remove a ball you change the population numbers, which changes the probability of getting a red or white ball. Since the population is much larger than the sample, however, the change in p from event to event is insignificant. As a rule, the population should be at least 20 times larger than the sample.

Cassidy can shoot free throws with 75% accuracy (she makes 75% of her shots). If she attempts 25 free throws, what's the probability she'll make at least 20?

P(x = 20) + P(x = 21) + P(x = 22) + P(x = 23) + P(x = 24) + P(x = 25) - P(20 or more) = P(x ≥ 20) = = P(x = 20) + P(x = 21) + P(x = 22) + P(x = 23) + P(x = 24) + P(x = 25) = 1 - P(x AP Statistics Semester 2 19) = 1 - .622 = .378. On a TI-83, this is 1-binomcdf(25,.75,19).

If a success is defined as getting a three on a six-sided number cube, what's P(x < 3) if you roll the number cube 10 times?

binomcdf(10,1/6,2) - In this situation, the number of 3s is a random variable with the distribution B (10,1/6,x). There are 10 independent trials, each with a 1/6 probability of success. So the random variable X can take on values 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10. We want to know P(X < 3), or the underlined numbers: 0 1 2 3 4 5 6 7 8 9 10 (0,1, and 2 are underlined) On your calculator, enter binomcdf(10,1/6,2) because you want 2 and below.