Lesson

Read the rule, then work each example: try the setup yourself, then tap to check one step at a time.

The rules

Binomial when: 2 outcomes · fixed n trials · independent (with replacement or a %) · same p each time. P(X) = C(n, X) · pˣ · (1 − p)ⁿ⁻ˣ.

P(X) = C(n, X) pˣ (1 − p)ⁿ⁻ˣ (P(X = x) = ₙCₓ pˣ qⁿ⁻ˣ)

Unusual if P < 0.05.
Guessing 20 questions, 5 choices (p = .2), at least 15 right = 1.8E−7 ≈ 0 → unlikely.

Translate the words into the lower and upper values before typing anything; 'between a and b' includes both ends.

exactly k → binomialpdf(n, p, k)
at most k (≤ k) → cdf lower 0, upper k
less than k (< k) → cdf lower 0, upper k − 1
at least k (≥ k) → cdf lower k, upper n
more than k (> k) → cdf lower k + 1, upper n
between a and b → cdf lower a, upper b (both ends in): 33 to 35 → .155 (exam Q30)

Example 1 · 2.8 #1a0/5

exactly 1 has brown eyes

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If 85% of all people have brown eyes and 6 people are selected at random, find the probability that

Notes: B = Brown Eyes N = No Brown Eyes

Round all answers to 6 decimal places

Try the setup yourself first, then tap.

Example 2 · 2.8 #1b0/7

at least 2 have brown eyes

N N N N N N
N B N N N N
N N B N N B
N B B N N B
N B N B B B
B N B B B B
B B B B B B

___

If 85% of all people have brown eyes and 6 people are selected at random, find the probability that

Notes: B = Brown Eyes N = No Brown Eyes

Round all answers to 6 decimal places

Try the setup yourself first, then tap.

Example 3 · 2.8 #1c0/5

at most 3 have brown eyes

N N N N N N
N B N N N N
N N B N N B
N B B N N B
N B N B B B
B N B B B B
B B B B B B

If 85% of all people have brown eyes and 6 people are selected at random, find the probability that

Notes: B = Brown Eyes N = No Brown Eyes

Round all answers to 6 decimal places

Try the setup yourself first, then tap.