Solve a problem

ProbabilityStatistics and probabilityHigh schoolabout 0:52

Independent events have P(A) = 0.2 and P(B) = 0.7. Find P(A and B) and P(A or B): animated lesson

A narrated, step-by-step probability video lesson with captions. Final answer: P(A and B) = 7/50 ≈ 0.14; P(A or B) = 19/25 ≈ 0.76; P(neither) = 6/25 ≈ 0.24.

SpeedLanguage

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
Independent events have P(A) = 0.2 and P(B) = 0.7. Find P(A and B) and P(A or B).
2. Step by step
1. $P(A \cap B) = P(A)P(B) = (\frac{1}{5})(\frac{7}{10}) = \frac{7}{50} \approx 0.14$
  Both: multiply, because the events are independent
2. $P(A \cup B) = \frac{1}{5} + \frac{7}{10} - \frac{7}{50} = \frac{19}{25} \approx 0.76$
  At least one: add and subtract the overlap
3. $P(A \cup B) - P(A \cap B) = \frac{31}{50} \approx 0.62$
  Exactly one of them
4. $(1 - P(A))(1 - P(B)) = \frac{6}{25} \approx 0.24$
  Neither
3. The answer
$P(A\cap B) = \frac{7}{50} \approx 0.14,\ P(A \cup B) = \frac{19}{25} \approx 0.76$
P(A and B) = 7/50 ≈ 0.14; P(A or B) = 19/25 ≈ 0.76; P(neither) = 6/25 ≈ 0.24
4. Check
- P(A or B) + P(neither) = 1 = 1.

Transcript

The problem. Here is the problem: Independent events have P(A) equals 0.2 and P(B) equals 0.7. Find P(A and B) and P(A or B). Two independent events A and B.

Step by step. Both: multiply, because the events are independent. At least one: add and subtract the overlap. Exactly one of them. Neither.

The answer. So the answer is P(A and B) equals 7 over 50 approximately 0.14; P(A or B) equals 19 over 25 approximately 0.76; P(neither) equals 6 over 25 approximately 0.24. For independent events the probability that both happen is the product of the individual probabilities.

Check. P(A or B) plus P(neither) equals 1 equals 1.

About probability

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

Independent events have P(A) = 0.2 and P(B) = 0.7. Find…