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X is binomial with n = 5 and p = 0.3. Find P(X = 2): animated lesson

A narrated, step-by-step probability video lesson with captions. Final answer: P(X = 2) ≈ 0.3087 (30.87%).

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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 (0.3 MB) · Captions (WebVTT)

Steps on screen

1. The problem
Worked example
X is binomial with n = 5 and p = 0.3. Find P(X = 2).
2. Step by step
1. $P(X = j) = \binom{5}{j} (\frac{3}{10})^{j} (\frac{7}{10})^{5 - j}$
  Binomial probability of exactly j successes
2. $\binom{5}{2} = 10,\quad P(X = 2) \approx 0.3087$
  Substitute j = 2
3. $\mu = np = 1.5,\quad \sigma = \sqrt{np(1-p)} \approx 1.0246951$
  Mean and standard deviation of the distribution
3. The answer
$P(X = 2) \approx 0.3087$
P(X = 2) ≈ 0.3087 (30.87%)
4. Check
- All binomial probabilities for j = 0..5 add to 1.

Transcript

The problem. Here is the problem: X is binomial with n equals 5 and p equals 0.3. Find P(X equals 2). Binomial: k successes in n trials.

Step by step. Binomial probability of exactly j successes. Substitute j equals 2. Mean and standard deviation of the distribution.

The answer. So the answer is P(X equals 2) approximately 0.3087 (30.87 percent). With 5 independent trials and success probability 3 over 10 per trial, the requested probability is about 30.87 percent.

Check. All binomial probabilities for j equals 0..5 add to 1.

About probability

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

X is binomial with n = 5 and p = 0.3. Find P(X = 2) (Lesson)