You toss tails and roll an even number ( when you toss a coin and roll a number cube)
Find the probability.
I thought It was 1/3 but I think that is wrong.
prob(tail and even) = (1/2)(3/6) = (1/2)(1/2) = 1/4
proof:
cases:
t1 t2 t3 t4 t5 t6
h1 h2 h3 h4 h5 h6 ---- 12 of those
tail and even:
t2 t4 t6 ----- 3 of those
prob = 3/12 = 1/4
explain why you thought it was 1/3.
To find the probability of tossing tails and rolling an even number, you need to consider the total number of possible outcomes for both events, as well as the number of desired outcomes.
First, let's determine the number of possible outcomes for each event:
- When tossing a coin, there are two possible outcomes: heads or tails.
- When rolling a number cube, there are six possible outcomes: 1, 2, 3, 4, 5, or 6.
Since you want to determine the probability of both events occurring, you need to multiply the number of possible outcomes together. Therefore, the total number of possible outcomes is 2 (coin toss) multiplied by 6 (number cube roll), which equals 12.
Next, let's determine the number of desired outcomes:
- Tossing tails occurs in 1 out of the 2 possible outcomes (since there is only one tail).
- Rolling an even number occurs in 3 out of the 6 possible outcomes (even numbers are 2, 4, and 6).
To find the number of desired outcomes for both events, multiply the number of desired outcomes together. Therefore, the number of desired outcomes is 1 (tails) multiplied by 3 (even numbers), which equals 3.
Finally, calculate the probability by dividing the number of desired outcomes by the total number of possible outcomes:
Probability = Number of desired outcomes / Total number of possible outcomes
Probability = 3 / 12
Probability = 1/4
Therefore, the correct probability of tossing tails and rolling an even number is 1/4 or 25%.