Question

3. Rolling a Die: If a die is rolled one time, find these probabilities. 

a. Getting a 2 

b. Getting a number greater than 6 

c. Getting an odd number 

d. Getting an odd or even number

Answer 1

When we roll a die, we can obtain six possible outcomes: 1, 2, 3, 4, 5, 6.

The probability of getting one of these outcomes equals $\frac{1}{6}.$

(a) $P(X=2)=\frac{1}{6}.$

(b) $P(X>6)=0,$ this is impossible event.

(c) $P(X \: is \: odd)=P(X\in\{1, 3, 5\})=\frac{3}{6}=\frac{1}{2}.$

(d) $P(X \: is \: odd \: or \: even)=P(X\in\{1, 3, 5\})+P(X\in\{2, 4, 6\})=\frac{3}{6}+\frac{3}{6}=1.$

Answer: (a) $\frac{1}{6}$ (b) 0 (c) $\frac{1}{2}$ (d) 1