Question

If two dice are rolled one time find the probability A 3 on one die or both dice

Answer 1

Answer:

$P=\frac{13}{36}=0.361$

Step-by-step explanation:

There are six possible outcomes when rolling a die. Therefore the probability of obtaining a 3 is a given is

$P = \frac{1}{6}$.

When throwing the two dice together, the probability of obtaining a 3 is the same:

$P_1 = \frac{1}{6} * \frac{5}{6} + \frac{5}{6} * \frac{1}{6}=\frac{5}{18}$

Since the events are independent then the probability of obtaining a three in both dice is:

$P_2 = \frac{1}{6} * \frac{1}{6} = \frac{1}{12}$.

Finally the probability of obtaining a 3 on a given or both is equal to the sum of the probabilities $P_1$ and $P_2$

$P=\frac{1}{12}+\frac{5}{18}=\frac{13}{36}=0.361$

Answer 2

$|\Omega|=6^2=36\\|A|=1\cdot5\cdot2+1=11\\\\P(A)=\dfrac{11}{36}\approx30.6\%$