Combined events and tree diagrams Quiz

1. A fair coin is tossed and a fair die is rolled. Find the probability of heads and a $5$.

• A. $\frac{2}{3}$
• B. $\frac{7}{12}$
• C. $\frac{1}{12}$
• D. $\frac{1}{8}$

2. A bag has $3$ red and $2$ green counters. Two are taken without replacement. Find the probability that both are red.

• A. $\frac{3}{10}$
• B. $\frac{9}{25}$
• C. $\frac{3}{5}$
• D. $\frac{2}{5}$

3. $A$ and $B$ are mutually exclusive with $P(A)=0.3$ and $P(B)=0.45$. Find $P(A\text{ or }B)$.

• A. $0.135$
• B. $0.15$
• C. $0.25$
• D. $0.75$

4. The probability of rain on any day is $0.4$, independently each day. Find the probability of at least one rainy day in three days.

• A. $0.064$
• B. $0.784$
• C. $0.216$
• D. $1.2$

5. Which pair of events is independent?

• A. Taking two sweets from a bag one after the other and eating the first
• B. Choosing a class president and then a vice-president, who must be a different student
• C. Tossing a coin and rolling a die
• D. Drawing two cards from a pack without replacing the first