Question

the table below shows the possible outcomes of rolling a six - sided number cube and flipping a coin.
1 2 3 4 5 6
h h1 h2 h3 h4 h5 h6
t t1 t2 t3 t4 t5 t6
what is the probability of getting a number less than 3 and a tails?
\\(\frac{1}{12}\\)
\\(\frac{1}{6}\\)
\\(\frac{1}{4}\\)

Explanation:

Step1: Determine total number of outcomes

There are 6 outcomes for rolling a cube and 2 outcomes for flipping a coin. So the total number of combined - outcomes is $6\times2 = 12$.

Step2: Identify favorable outcomes

Numbers less than 3 on the cube are 1 and 2. When the coin shows tails (T), the favorable outcomes are T1 and T2. So there are 2 favorable outcomes.

Step3: Calculate probability

The probability $P$ of an event is given by the formula $P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$. So $P = \frac{2}{12}=\frac{1}{6}$.

Answer:

$\frac{1}{6}$