To find the probability of a coin landing on tails (T) and then rolling an odd number on a number cube, follow these steps:
Step 1: Determine the sample space
First, determine the sample space for both the coin flip and the number cube. The sample space for a coin flip is {H, T} (where H stands for heads and T stands for tails), and the sample space for a number cube roll is {1, 2, 3, 4, 5, 6}.
Step 2: Calculate the events
Next, calculate the events that satisfy the condition of landing on T (tails) and rolling an odd number. From the sample spaces, the event of getting tails on the coin flip is {T}, and the event of rolling an odd number on the number cube is {1, 3, 5}.
Step 3: Compute the probabilities
To calculate the probability of both events occurring, multiply the probabilities of each event happening. The probability of landing on tails is 1/2, and the probability of rolling an odd number is 3/6 (since there are three outcomes out of six that are odd).
Step 4: Calculate the final probability
Multiply the probabilities of both events to find the final probability.
P(T then odd) = (1/2) * (3/6) = 1/4
Therefore, the probability of flipping a coin and rolling an odd number on a number cube, given that it landed on tails, is 1/4 or 0.25.