Question

You roll a 20-sided die and a 6-sided die. What is the probability that the sum of the dice is less than 5?
a) 5%
b) 4%
c) 3%
d) 2%

Answer 1

Answer:

Probability that the sum of dice is less than 5: a) 5%.

Step-by-step explanation:

Probability of an Event:

$\boxed{Probability\ (P(X))=\frac{event's\ outcomes\ (n(X))}{total\ outcomes\ (n(S))} }$

Let:

A = number shown on 20-sided die

B = number shown on 6-sided die

S = combination of A and B

X = sum of both dice is less than 5

Then:

A = {1, 2, 3, ... , 20}

n(A) = 20

B = {1, 2, 3, ... , 6}

n(B) = 6

Since event A and event B are independent, therefore:

n(S) = n(A) × n(B)

      = 20 × 6

      = 120

X = {(1,1), (1,2), (1,3), (2,1), (2,2), (3,1)}

n(X) = 6

$\displaystyle P(X)=\frac{n(X)}{n(S)}$

         $\displaystyle=\frac{6}{120}$

         $=0.05$

         $=0.05\times100\%$

         $=5\%$