BINS
The "B" in the BINS acronym stands for this requirement.
Binary
Evaluate nCn for any positive integer n.
1
A student guesses randomly on a 4-question true/false quiz. This is the expression setup for getting exactly 3 questions right.
4C3 * .253 * .751
A factory inspects 200 lightbulbs with a 3% defect rate. Calculate the expected number (mean) of defective bulbs.
6
A basketball player makes 80% of her free throws. If she shoots 10 free throws, this is her expected number of made shots.
8
The "I" in BINS ensures that the outcome of one trial does not affect the outcome of another.
Independent
Evaluate 5C2 without using a calculator.
10
A medical test is 90% accurate (p = 0.90). For a sample of n = 5 patients, calculate the exact probability that all 5 test correctly.
.5905 or 59.05%
A bowler makes a strike 60% of the time. If he bowls 50 frames, calculate the variance of his strikes.
12
A disease affects 10% of a population. If 3 people are tested independently, this is the probability that all 3 test positive.
.001
The "N" in BINS specifies that this must be set before conducting the experiment.
Number of trials
Evaluate 7C2 without a calculator
21
A coin is flipped 3 times. Calculate the exact probability of getting exactly 1 Head.
.375 or 37.5%
Calculate the standard deviation of correct answers for a student who guesses on 100 4-option multiple-choice questions (p = 0.25).
4.33
A tech manufacturer knows that 2% of microchips produced on an assembly line are defective. In a random quality-check sample of n = 50 microchips, what is the exact probability that at most 1 chip is defective?
.7358
The "S" in BINS requires that p, the probability of success, must have this property across all trials.
Same probability
A 6-question quiz is given. Calculate the number of distinct ways a student can get exactly 4 questions correct and 2 wrong.
15
An archer hits a bullseye 80% of the time. In 4 shots, this is the exact probability she hits the target exactly 2 times.
.1536
A roulette wheel is spun 400 times. The probability of landing on red is 18/38. Calculate the mean number of red outcomes.
189.47
A new allergy medication has a success rate of p = 0.70. If a doctor prescribes the drug to n = 6 patients, what is the probability that at least 5 patients experience relief?
.4202
A bowler rolls 10 frames. After every strike, her confidence rises and her probability of getting another strike increases for the next frame. State which specific BINS condition this scenario violates and why.
S or I
Because of symmetry in combinations,10C7 is equal to 10Cr. What is the value of r?
3
A machine has a 10% error rate (p = 0.10). In a batch of n = 3 items, set up the complete addition expression needed to calculate P(X <= 1)
3C0 (.10)0 (.90)3 + 3C1 (.10)1 (.90)2
A binomial random variable X has a mean = 12 and variance = 3. Find the probability of success (p).
.75
An e-commerce website has an average sales conversion rate of 10% (p = 0.10) per visitor. If 5 visitors browse the site independently, what is the probability that at least 1 visitor makes a purchase?
.4095