Question

If you have two six-sided die each labelled one throgh six. Which set of independent events has a higher probabllity?

Answer 1

SOLUTION

We will consider all the sets of probabilities, the one with the highest probability is the right answer.

a) You roll an odd number and roll a 5: the probability is calculated thus:

$\begin{gathered} \frac{3}{6}\times\frac{1}{6} \\ =\frac{3}{36} \\ =\frac{1}{12} \\ =0.0833 \end{gathered}$

b) You land on an odd number or you roll a 6: the probability is calculated thus:

$\begin{gathered} \frac{3}{6}+\frac{1}{6} \\ =\frac{4}{6} \\ =\frac{2}{3} \\ =0.6667 \end{gathered}$

c) You roll a six and roll a 4: the probability is calculated thus:

$\begin{gathered} \frac{1}{6}\times\frac{1}{4} \\ =\frac{1}{24} \\ =0.0417 \end{gathered}$

d) You roll a 3 and roll an old number: the probability is calculated thus:

$\begin{gathered} \frac{1}{6}\times\frac{3}{6} \\ =\frac{3}{36} \\ =\frac{1}{12} \\ =0.0833 \end{gathered}$

Now, comparing all the probabilities, the set of independent events with the highest probability is the event of You land on an odd number or you roll a 6.

Therefore the correct answer is B.