Modelling with probability Quiz

1. Which assumption is needed to model the number of heads in 20 tosses as $B(20,0.5)$?

• A. The tosses are independent and the coin is fair
• B. The coin lands heads at most 10 times
• C. The tosses alternate between heads and tails
• D. Each toss has probability $0.5$ of being a tail only

2. A die is thought to be biased. In 120 rolls a six appears 20 times. What is the expected number of sixes for a fair die?

• A. $10$
• B. $20$
• C. $30$
• D. $6$

3. Students in one class are sampled to model who has a mobile phone with $p=0.9$ each, independently. Which criticism is best?

• A. $p$ is too large to be a probability
• B. The sample is too large
• C. Students in one class may share similar backgrounds, so independence may not hold
• D. Phones cannot be modelled by a binomial distribution

4. $X\sim B(5,0.2)$. Which is $P(X=2)$?

• A. $10\times0.2^3\times0.8^2$
• B. $5\times0.2^2\times0.8^3$
• C. $0.2^2\times0.8^3$
• D. $10\times0.2^2\times0.8^3$

5. A model says the probability of rain on any day is $0.3$, independently. Which is a more realistic refinement?

• A. Rain has probability $1$ each day
• B. Rain cannot occur two days running
• C. The probability of rain is $0$ in summer
• D. Rain tomorrow is more likely if it rained today