Starter quiz
- Event A is ______ of event B if the probability of event A occurring is not affected by whether or not event B occurs.
- 'independent' ✓
- Select the example of events which are not independent.
- Rolling a die and then flipping a coin
- Flipping three coins together
- Rolling two dice together
- Taking a counter at random from a box, replacing it and then taking another
- Taking a counter at random from a box, keeping it and then taking another ✓
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The table shows the types of marble in a bag. Match each event to its probability.- P(blue)⇔✓
- P(green)⇔✓
- P(blue and has no swirl)⇔✓
- P(blue given it has no swirl)⇔✓
- P(green and has a swirl)⇔✓
- P(green given it has swirl)⇔✓
- A marble is taken at random from a box of marbles. Alex works out that P(swirl given it is blue) = P(swirl). This shows the event 'has a swirl' is __________ of the event 'blue marble'.
- conditional
- exhaustive
- independent ✓
- mutually exclusive
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- A 10-sided die with integers from 1 to 10 written on it is rolled once. Select the pair of mutually exclusive events.
- A factor of 9 ✓
- A factor of 10
- Even number ✓
- Odd number
- Prime number
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A deck of cards has a number on it (either prime or non-prime), and a symbol (a circle, square, or wave). A card is selected at random from the deck. Find P(non-prime | wave).- ✓
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Exit quiz
- Event A and event B are mutually exclusive events. Which of these statements are correct?
- P(A and B) = 0 ✓
- P(A or B) = 0
- P(B | A) = 0 ✓
- P(A | B) = 0 ✓
- P(A) + P(B) = 0
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From the frequency Venn diagram, P(A | B) =______. Give your answer as a decimal.- '0.7' ✓
- From the frequency Venn diagram, P(A | B') = ______. Give your answer as a decimal.
- '0.7' ✓
- The diagram shows the number of outcomes for two events A and B. The values of P(A | B) and P(A | B') show that events A and B are ______ events.
- 'independent' ✓
Here is an incomplete frequency Venn diagram. P(C) = , P(D') = , P(C ∩ D) = and P(C | D) = . The value of is ______.- '10' ✓
- Here is an incomplete frequency Venn diagram. P(C) = , P(D') = , P(C ∩ D) = and P(C | D) = . The value of is ______.
- '70' ✓
Worksheet
Presentation
Video
Lesson Details
Key learning points
- A Venn diagram can be used to calculate conditional probabilities
- A Venn diagram can be used to calculate conditional probabilities involving sets of events
- Venn diagrams allow us to identify which events are mutually exclusive
- Venn diagrams can be used to identify which events are independent
Common misconception
Pupils may confuse the probability of event A given B, P(A|B), with the probability of event A and B occurring.
Use the context of the question to make a judgement about what probability is to be calculated. Try to avoid using, or draw attention to, potentially ambiguous language/notation. E.g. Is P(AB) referring to P(A given B) or P(B given A) or P(A and B)?
Keywords
Venn diagram - Venn diagrams are a representation used to model statistical/probability questions. Commonly circles are used to represent events.
Probability - The probability that an event will occur is the proportion of times the event is expected to happen in a suitably large experiment.
Conditional probability - Conditional probability is the probability of an outcome occurring given that another event has occurred.
Independent events - Event A is independent of event B if the probability of event A occurring is not affected by whether or not event B occurs.
Mutually exclusive - Mutually exclusive events have no outcomes in common.