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X is binomial with n = 10 and p = 0.5. Find P(X ≥ 8): animated lesson

A narrated, step-by-step probability video lesson with captions. Final answer: P(X ≥ 8) ≈ 0.0546875 (5.46875%).

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Video with a synthetic English voice and captions. Pick another language for subtitles in that language, or open the interactive version.

Video narrated by a synthetic voice (Piper TTS, en_US-ljspeech-high voice (LJ Speech dataset, public domain)); the steps come from our maths engine and the answer was checked independently. Download MP4 (0.4 MB) · Captions (WebVTT)

Steps on screen

1. The problem
Worked example
X is binomial with n = 10 and p = 0.5. Find P(X ≥ 8).
2. Step by step
1. $P(X = j) = \binom{10}{j} (\frac{1}{2})^{j} (\frac{1}{2})^{10 - j}$
  Binomial probability of exactly j successes
2. $P(X \ge 8) = \sum_{j=8}^{10} P(X = j) \approx 0.0546875$
  Add the terms for j = 8 to 10
3. $\mu = np = 5,\quad \sigma = \sqrt{np(1-p)} \approx 1.5811388$
  Mean and standard deviation of the distribution
3. The answer
$P(X \ge 8) \approx 0.0546875$
P(X ≥ 8) ≈ 0.0546875 (5.46875%)
4. Check
- All binomial probabilities for j = 0..10 add to 1.

Transcript

The problem. Here is the problem: X is binomial with n equals 10 and p equals 0.5. Find P(X greater than or equal to 8). Binomial: k successes in n trials.

Step by step. Binomial probability of exactly j successes. Add the terms for j equals 8 to 10. Mean and standard deviation of the distribution.

The answer. So the answer is P(X greater than or equal to 8) approximately 0.0546875 (5.46875 percent). With 10 independent trials and success probability 1 over 2 per trial, the requested probability is about 5.46875 percent.

Check. All binomial probabilities for j equals 0..10 add to 1.

About probability

Probability of single events, complements, independent events and binomial outcomes.

X is binomial with n = 10 and p = 0.5. Find P(X ≥ 8)