Modelling with probability Quiz

1. A coin is tossed three times and the model assumes independent tosses with $P(H)=0.5$. Find $P(\text{exactly two heads})$.

• A. $\frac18$
• B. $\frac38$
• C. $\frac12$
• D. $\frac34$

2. Which assumption allows the probabilities of repeated trials to be multiplied?

• A. Outcomes are equally likely
• B. Trials are mutually exclusive
• C. The probabilities are all $0.5$
• D. The trials are independent

3. A model assumes each of five days is dry with probability $0.7$, independently. In reality dry days come in spells. What is the effect on $P(\text{five dry days})$?

• A. The model probably underestimates it
• B. The model probably overestimates it
• C. The model gives exactly the right value
• D. There is no effect on any probability

4. A bag has 5 red and 5 blue counters. Two are taken without replacement. Find $P(\text{both red})$.

• A. $0.25$
• B. $0.222$
• C. $0.2$
• D. $0.5$

5. Which change makes a model more realistic?

• A. Assuming all students are identical
• B. Using the same probability every day
• C. Letting the probability change with weather or season
• D. Ignoring data that disagree with the model