Question

A standard number cube is tossed. Find the probability of getting P(greater than 2 or less than 4).1/215/66

Answer 1

The probability of getting P(greater than 2 or less than 4) is given by

because the a number greater than 2 and less than 4 is 3.

Since the cube has 6 faces, the probability of getting one face is 1/6, then we have

`\begin{gathered} \text{P(greater than 2)}=P(3)+P(4)+P(5)+P(6) \\ \text{P(greater than 2)}=(1)/(6)+(1)/(6)+(1)/(6)+(1)/(6) \\ \text{P(greater than 2)}=(4)/(6) \end{gathered}`

Similarly,

`\begin{gathered} P(\text{less than 4)}=P(3)+P(2)+P(1) \\ P(\text{less than 4)}=(1)/(6)+(1)/(6)+(1)/(6) \\ P(\text{less than 4)}=(3)/(6) \end{gathered}`

since P(3)= 1/6, we have

`\begin{gathered} P(\text{greater than 2 OR less than 4)=P(greater than 2)}+P(\text{less than 4)-P(3)} \\ P(\text{greater than 2 OR less than 4)=}(4)/(6)+(3)/(6)-(1)/(6) \end{gathered}`

which gives

`P(\text{greater than 2 OR less than 4)=}(7-1)/(6)=(6)/(6)=1`

Therefore, the answer is 1.