A penny is tossed and a number cube is rolled. Find each probability. 26. $$ P $$ (heads and 4 ) 27. $$ P $$ (tails and 1 ) 28. $$ P $$ (tails and odd number) 29. $$ P $$ (heads and a number greater than 2 ) 30. $$ P $$ (tails and a number less than or equal to 5 )

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UpStudy AI · Accepted Answer

1. For a coin toss and a number cube roll, the total sample space has $$2 \times 6 = 12$$ equally likely outcomes.

2. For each event, we consider the probability of the coin outcome multiplied by the probability of the cube outcome.

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**26. $$ P(\text{heads and } 4) $$**  
- Probability of heads: $$\frac{1}{2}$$.  
- Probability of rolling 4: $$\frac{1}{6}$$.  
- Combined probability:  
  $$
  \frac{1}{2} \times \frac{1}{6} = \frac{1}{12}.
  $$

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**27. $$ P(\text{tails and } 1) $$**  
- Probability of tails: $$\frac{1}{2}$$.  
- Probability of rolling 1: $$\frac{1}{6}$$.  
- Combined probability:  
  $$
  \frac{1}{2} \times \frac{1}{6} = \frac{1}{12}.
  $$

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**28. $$ P(\text{tails and odd number}) $$**  
- Probability of tails: $$\frac{1}{2}$$.  
- The odd numbers on a cube are: 1, 3, 5, so there are 3 favorable outcomes out of 6. Thus,  
  $$
  P(\text{odd number}) = \frac{3}{6} = \frac{1}{2}.
  $$  
- Combined probability:  
  $$
  \frac{1}{2} \times \frac{1}{2} = \frac{1}{4}.
  $$

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**29. $$ P(\text{heads and a number greater than } 2) $$**  
- Probability of heads: $$\frac{1}{2}$$.  
- Numbers greater than 2 on the cube are: 3, 4, 5, 6, so there are 4 favorable outcomes out of 6. Thus,  
  $$
  P(\text{greater than } 2) = \frac{4}{6} = \frac{2}{3}.
  $$  
- Combined probability:  
  $$
  \frac{1}{2} \times \frac{2}{3} = \frac{1}{3}.
  $$

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**30. $$ P(\text{tails and a number less than or equal to } 5) $$**  
- Probability of tails: $$\frac{1}{2}$$.  
- Numbers less than or equal to 5 on the cube are: 1, 2, 3, 4, 5, so there are 5 favorable outcomes out of 6. Thus,  
  $$
  P(\text{less than or equal to } 5) = \frac{5}{6}.
  $$  
- Combined probability:  
  $$
  \frac{1}{2} \times \frac{5}{6} = \frac{5}{12}.
  $$
- $$ P(\text{heads and } 4) = \frac{1}{12} $$ - $$ P(\text{tails and } 1) = \frac{1}{12} $$ - $$ P(\text{tails and odd number}) = \frac{1}{4} $$ - $$ P(\text{heads and a number greater than } 2) = \frac{1}{3} $$ - $$ P(\text{tails and a number less than or equal to } 5) = \frac{5}{12} $$

A penny is tossed and a number cube is rolled. Find each probability. 26. \( P \) (heads and 4 ) 27. \( P \) (tails and 1 ) 28. \( P \) (tails and odd number) 29. \( P \) (heads and a number greater than 2 ) 30. \( P \) (tails and a number less than or equal to 5 )

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