Binomial Breakdown Worksheet slice edition CARD 01
Binomial Breakdown
Part 1: BINS Criteria
1. Define the four requirements for a binomial setting:
B:
I:
N:
S:
CARD 02
2. Scenario Check
"A student picks a card from a deck, records the suit, and replaces it. They repeat this 10 times. Find the probability of exactly 3 Hearts."
Does this meet BINS? Explain:
CARD 03
3. Parameter Identification
"A quality engineer inspects 50 microchips. 4% are defective. Find the probability that fewer than 5 are defective."
n
p
k (Boundary)
CARD 04
4. Boundary Logic
In Card 03, why did you choose your specific value for k ? Explain the logic for finding "fewer than 5" in a discrete setting.
CARD 05
5. Exact Match
Basketball player: 75% accuracy. 8 shots. Probability of exactly 6 ?
Modern Spreadsheet Formula
=BINOM.DIST(
P = ______
CARD 06
6. Cumulative "At Most"
Guessing on 10-question quiz (4 options). Probability of at most 3 correct?
Modern Spreadsheet Formula
=BINOM.DIST(
P = ______
CARD 07
7. Greater Than
60% own pets. Sample of 15. Probability that more than 10 own a pet?
k logic: k = ____
=1 - BINOM.DIST(
P = ______
CARD 08
8. Setting Violations
Selecting 5 students from a class of 30 without replacement . Why does this fail BINS?
CARD 09
9. Overbooked Flight
"20 tickets sold. 19 seats. 95% show up. Probability the flight is overbooked?"
k logic: k = ____
=BINOM.DIST(
P = ______
CARD 10
10. Range Logic
100 lightbulbs. 2% failure rate. Find the probability that between 1 and 3 (inclusive) are defective.
Step 1: Range Logic (Symbolic)
P(X ≤ ) - P(X ≤ )
Modern Spreadsheet Formula
=
CARD 11
11. At Least k
Medical trial success = 80%. 20 patients. Probability that at least 15 are cured?
k logic: k = ____
=1 - BINOM.DIST(
P = ______
CARD 12
12. SCRAP Analysis
"Find the probability that more than 2 items are SCRAP in a sample of 25 (90% are GOOD)."
n
p (Scrap)
k
Modern Sheets Formula
=
CARD 13
13. Digital Marketing
"15% social media click rate. Sample of 200 followers. Probability that exactly 30 click?"
Formula
=
P = ______
CARD 14
14. Election Polling
"Candidate support = 48%. Survey 100 voters. Probability that fewer than 45 support them?"
Formula
=
P = ______
CARD 15
15. Streaming Trends
"70% use a specific service. Survey 30. Probability that between 20 and 25 use it?"
Range Logic
P(X ≤ ) - P(X ≤ )
Sheets Formula
=
CARD 16
16. Decoding Theory
P(X = k) = (nCk) • pk • (1 - p)n - k
In a real-world scenario, what does the (1 - p)n - k part represent?
CARD 17
17. Manual Setup
"Scenario: A fair coin is flipped 5 times. Find the prob. of getting exactly 3 heads."
(
C
)
•
(
)
•
(
)
Complete the formula using (nCk) notation
CARD 18
Mastery Challenge
Describe a scenario that meets B, I, and N, but violates S (Constant Probability). Explain the fix.
KEY 01
Answer: Card 01
B: Binary (Success/Failure)
KEY 02
Answer: Card 02
YES.
Replacement ensures independence (I) and constant probability (S). Trials n=10, Success=Heart.
KEY 03
Answer: Card 03
n
50
p
0.04
k
4
Binomial Breakdown Answer Key KEY 01
KEY 01. BINS Criteria
B: Binary (Success/Fail)
N: Fixed Trials (n)
KEY 02
KEY 02. Check
YES.
Replacement ensures constant probability (S) and independence (I). Fixed trials n=10. Binary (Heart/Not).
KEY 03
KEY 03. Parameters
n=50
p=0.04
k=4
KEY 04
KEY 04. Boundary Logic
"Fewer than 5" targets outcomes 0, 1, 2, 3, 4. Modern BINOM.DIST cumulative calculates P(X ≤ k), so we must use k=4.
KEY 05
KEY 05. Exact Match
=BINOM.DIST(6, 8, 0.75, FALSE)
0.3115
KEY 06
KEY 06. Cumulative
=BINOM.DIST(3, 10, 0.25, TRUE)
0.7759
KEY 07
KEY 07. Greater Than
=1 - BINOM.DIST(10, 15, 0.6, TRUE)
0.2173
KEY 08
KEY 08. Violations
FAIL: INDEPENDENT (I)
No replacement from a small population (30) changes probability significantly for each subsequent pick.
KEY 09
KEY 09. Overbooked
=BINOM.DIST(20, 20, 0.95, FALSE)
0.3585
KEY 10
KEY 10. Range Logic
P(X≤3) - P(X≤0)
=BINOM.DIST(3, 100, .02, T) - BINOM.DIST(0, 100, .02, T)
0.7225
KEY 11
KEY 11. At Least k
=1 - BINOM.DIST(14, 20, 0.8, TRUE)
0.8042
KEY 12
KEY 12. SCRAP Case
Success = SCRAP (p=0.10)
=1 - BINOM.DIST(2, 25, 0.1, TRUE)
0.4629
KEY 13
KEY 13. Digital Mktg
=BINOM.DIST(30, 200, 0.15, FALSE)
0.0772
KEY 14
KEY 14. Polling
=BINOM.DIST(44, 100, 0.48, TRUE)
0.2403
KEY 15
KEY 15. Trends Range
P(X≤25) - P(X≤19)
=BINOM.DIST(25, 30, .7, T) - BINOM.DIST(19, 30, .7, T)
0.6865
KEY 16
KEY 16. Theory Decode
Represents probability of Failures occurring. (1-p) is the chance of one fail; (n-k) is the number of trials that must be failures.
KEY 17
KEY 17. Setup Answer
Binomial Breakdown Slides Stats Lab
Binomial Breakdown
Mastering criteria and digital calculations.
THE BINS TEST
Four requirements for every binomial setting.
B
Binary
Two outcomes (Success/Failure).
I
Independent
Trials don't affect each other.
N
Number
A fixed number of trials.
S
Success
Prob. stays constant (p).
THE FOUNDATION
The mathematics powering the tools.
P(X = k) =
nk
• pk • (1 - p)n - k
nCk
Ways
Combinations of successes.
pk
Successes
Probability of k successes.
(1-p)n-k
Failures
Probability of the remaining failures.
FORMULA DRILL
In the exact hand-formula, what does the exponent n - k represent?
The total number of failures.
NUMERICAL SETUP
5 COIN FLIPS
"Probability of getting exactly 3 heads?"
P(X=3) =
53
• (0.5)3 • (0.5)2
CLASS DRILL
"Fill in the expression for exactly 3 heads in 5 flips:"
(
C
) • (
)
• (
)
CALCULATION STATION
EXACT MATCH
Exactly 6 makes out of 8 shots (p=0.75)
BINOM.DIST(6, 8, 0.75, FALSE)
MORE THAN
More than 10 pets in 15 houses (p=0.60)
1 - BINOM.DIST(10, 15, 0.6, TRUE)
PRO CHEAT SHEET
FALSE
Exactly k
TRUE
At Most k
1 - TRUE
More Than k
KEEP MODELING
Binomial Case Cards Binomial Case Cards
Task Cards & Scenario Bank
Activity Resource
Task Card Instructions: Cut along the dashed lines. For each scenario, students must identify n , p , k , and write the Google Sheets Formula . Perfect for small group stations or individual drill practice.
CARD 01
Shopping Spree
A retail store knows that 25% of visitors make a purchase. If 80 people visit the store today, what is the probability that exactly 20 make a purchase?
n: ______
p: ______
k: ______
Formula:
CARD 02
Safety Check
A car safety feature has a failure rate of 0.1%. In a shipment of 5,000 cars, what is the probability that at least 1 car has a faulty feature?
n: ______
p: ______
k: ______
Formula:
CARD 03
App Usage
65% of students use a study app. If you interview 40 students, what is the probability that between 25 and 30 (inclusive) use the app?
n: ______
p: ______
k: ______
Formula:
CARD 04
Cafe Orders
A cafe finds that 40% of customers order a pastry. In a group of 12 customers, what is the probability that more than 5 order a pastry?
n: ______
p: ______
k: ______
Formula:
CARD 05
Shipping
98% of packages arrive on time. Out of 150 packages, what is the probability that at most 145 arrive on time?
n: ______
p: ______
k: ______
Formula:
CARD 06
Germination
A seed packet has a 90% germination rate. If you plant 100 seeds, what is the probability that fewer than 85 sprout?
n: ______
p: ______
k: ______
Formula:
CARD 07
Ad Recall
30% recall an ad. If 200 watch, what is the probability that exactly 65 recall it?
n: ______
p: ______
k: ______
Formula:
CARD 08
Daily Storms
There is a 40% chance of rain. Over a 30-day month, what is the probability that it rains
