think of tossing a penny and rolling a die. 1. How many events are possible? 2. What is $$ P(H, 4) $$ ? 3. What is $$ P(T $$, an even number)? 4. What is $$ P(T $$, a factor of 30$$ ) $$ ? 5. What is $$ P(H $$, number $$ 3) $$ ? 6. What is $$ P(T $$, an odd number)? 7. What is $$ P(T $$, not 4$$ ) $$ ? 8. What is $$ P(H $$, prime number)? 9. What is $$ P(H, 1 $$ or 6$$ ) $$ ? 10. What is $$ P(H $$, factor of 45$$ ) $$ ?

Question

think of tossing a penny and rolling a die. 1. How many events are possible? 2. What is $$ P(H, 4) $$ ? 3. What is $$ P(T $$, an even number)? 4. What is $$ P(T $$, a factor of 30$$ ) $$ ? 5. What is $$ P(H $$, number $$ >3) $$ ? 6. What is $$ P(T $$, an odd number)? 7. What is $$ P(T $$, not 4$$ ) $$ ? 8. What is $$ P(H $$, prime number)? 9. What is $$ P(H, 1 $$ or 6$$ ) $$ ? 10. What is $$ P(H $$, factor of 45$$ ) $$ ?

UpStudy AI · Accepted Answer

1. The possible outcomes come from tossing a coin (2 outcomes: $$ H $$ or $$ T $$) and rolling a die (6 outcomes: $$ 1, 2, 3, 4, 5, 6 $$). Thus, the total number of outcomes is
   $$
   2 \times 6 = 12.
   $$

2. $$ P(H,4) $$ is the probability of getting $$ H $$ on the coin and $$ 4 $$ on the die. Only one outcome is favorable: $$ (H,4) $$. Therefore,
   $$
   P(H,4) = \frac{1}{12}.
   $$

3. $$ P(T, \text{an even number}) $$:
   - Even numbers on the die: $$ 2, 4, 6 $$.
   - Favorable outcomes: $$ (T,2), (T,4), (T,6) $$ (3 outcomes).
   $$
   P(T, \text{even}) = \frac{3}{12} = \frac{1}{4}.
   $$

4. $$ P(T, \text{a factor of 30}) $$:
   - Factors of 30 among $$ 1 $$ to $$ 6 $$: $$ 1, 2, 3, 5, 6 $$ (note that $$ 4 $$ is not a factor).
   - Favorable outcomes: $$ (T,1), (T,2), (T,3), (T,5), (T,6) $$ (5 outcomes).
   $$
   P(T, \text{factor of } 30) = \frac{5}{12}.
   $$

5. $$ P(H, \text{number } > 3) $$:
   - Numbers greater than $$ 3 $$ on the die: $$ 4, 5, 6 $$ (3 outcomes).
   - Favorable outcomes: $$ (H,4), (H,5), (H,6) $$ (3 outcomes).
   $$
   P(H, >3) = \frac{3}{12} = \frac{1}{4}.
   $$

6. $$ P(T, \text{an odd number}) $$:
   - Odd numbers on the die: $$ 1, 3, 5 $$ (3 outcomes).
   - Favorable outcomes: $$ (T,1), (T,3), (T,5) $$ (3 outcomes).
   $$
   P(T, \text{odd}) = \frac{3}{12} = \frac{1}{4}.
   $$

7. $$ P(T, \text{not } 4) $$:
   - Numbers that are not $$ 4 $$ on the die: $$ 1, 2, 3, 5, 6 $$ (5 outcomes).
   - Favorable outcomes: $$ (T,1), (T,2), (T,3), (T,5), (T,6) $$ (5 outcomes).
   $$
   P(T, \text{not } 4) = \frac{5}{12}.
   $$

8. $$ P(H, \text{prime number}) $$:
   - Prime numbers on the die: $$ 2, 3, 5 $$ (3 outcomes).
   - Favorable outcomes: $$ (H,2), (H,3), (H,5) $$ (3 outcomes).
   $$
   P(H, \text{prime}) = \frac{3}{12} = \frac{1}{4}.
   $$

9. $$ P(H, 1 \text{ or } 6) $$:
   - Favorable die outcomes: $$ 1 $$ or $$ 6 $$ (2 outcomes).
   - Favorable outcomes: $$ (H,1) $$ and $$ (H,6) $$ (2 outcomes).
   $$
   P(H, 1 \text{ or } 6) = \frac{2}{12} = \frac{1}{6}.
   $$

10. $$ P(H, \text{factor of } 45) $$:
    - Factors of $$ 45 $$ among $$ 1 $$ to $$ 6 $$ are $$ 1, 3, 5 $$ (since $$ 9 $$ exceeds $$ 6 $$).
    - Favorable outcomes: $$ (H,1), (H,3), (H,5) $$ (3 outcomes).
    $$
    P(H, \text{factor of } 45) = \frac{3}{12} = \frac{1}{4}.
    $$
1. There are 12 possible outcomes. 2. $$ P(H,4) = \frac{1}{12} $$. 3. $$ P(T, \text{even}) = \frac{1}{4} $$. 4. $$ P(T, \text{factor of 30}) = \frac{5}{12} $$. 5. $$ P(H, >3) = \frac{1}{4} $$. 6. $$ P(T, \text{odd}) = \frac{1}{4} $$. 7. $$ P(T, \text{not } 4) = \frac{5}{12} $$. 8. $$ P(H, \text{prime}) = \frac{1}{4} $$. 9. $$ P(H, 1 \text{ or } 6) = \frac{1}{6} $$. 10. $$ P(H, \text{factor of } 45) = \frac{1}{4} $$.

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