Question

A six-sided number cube is rolled twice. Which expression can be used to find P(5, then3)? A. 1/5 x 1/3 B. 1/6 x 1/5 C. 5/6 x 3/6 D. 1/6 x 1/6

Answer 1

D. 1/6 chance to roll, say, a 6, but 2/36 chance or rather, 1/18 chance to roll 2 6's!

Answer 2

Answer:  The correct option is

(D) $\dfrac{1}{6}\times \dfrac{1}{6}.$

Step-by-step explanation:  Given that a six-sided number cube is rolled twice.

We are to select the expression that can be used to find the following probability :

$P(5,~then~3).$

Let S denote the sample space of drawing a number from a six-sided cube.

and let A and B represents the events of drawing 5 and 3 respectively from a six-sided cube.

Then,

$n(S)=6,~~n(A)=1,~~n(B)=1.$

So, the probabilities of events A and B are given by

$P(A)=\dfrac{n(A)}{n(S)}=\dfrac{1}{6},\\\\\\P(B)=\dfrac{n(B)}{n(S)}=\dfrac{1}{6}.$

Therefore, the probability P(5 then 3) is given by

$P(A)\times P(B)=\dfrac{1}{6}\times\dfrac{1}{6}.$

Thus, the required expression is $\dfrac{1}{6}\times \dfrac{1}{6}.$

Option (D) is CORRECT.