Question

If you roll a die, find the probability that you: (Enter your answers in exact form or round to 3 decimalplaces.)(a) roll at least 4 or an odd number,Answer:(b) roll an even number or a number at most 5.Answer:

Answer 1

A.

The question asks us to find the probability of getting at least 4 or an odd number after throwing a die.

This is easily gotten using the OR probability of two events which states:

`\begin{gathered} P(A\text{ OR B) = P(A) + P(B) - P(A AND B)} \\ \text{if A = rolling at least 4} \\ B\text{ = rolling odd number,} \\ \\ P(\text{rolling at least 4 OR rolling odd number) = } \\ P(\text{at least 4) + P(odd number) - P(at least 4 AND odd number)} \end{gathered}`

To get at least 4, it means the possible values we can have are: 4, 5, 6.

To get an odd number, it means the possible values we can have are: 1, 3, 5.

From both set of possibilities, 5 is common. We need to subtract the probability of getting a 5 in both situations to prevent duplication.

Thus, we can compute each probability:

`\begin{gathered} P(any\text{ number)= }(1)/(6) \\ \\ P(at\text{ least 4)= P(4) OR P(5) OR P(6) = P(4) + P(5) +P(6)} \\ \therefore P(at\text{ least 4)= }(1)/(6)+(1)/(6)+(1)/(6)=(3)/(6) \\ \\ P(\text{odd number) = P(1) OR P(3) OR P(5) = P(1)+P(3)+P(5)} \\ \therefore P(\text{odd number)= }(1)/(6)+(1)/(6)+(1)/(6)=(3)/(6) \\ \\ P(\text{at least 4 AND odd number) = }(1)/(6) \\ \\ \\ \therefore P(\text{at least 4 or odd number)=}(3)/(6)+(3)/(6)-(1)/(6)=(5)/(6) \end{gathered}`

Therefore, the probability of getting at least 4 or an odd number is 5/6

B:

This part of the question asks us to find the probability of rolling an even number or a number at most 5.

We, once again, take a look at the possibilities to solve this question.

Possibilities of getting an even number are: 2, 4, or 6

Possibilities of getting at most 5 are: 1, 2 , 3, 4, 5.

Therefore, we can compute the probabilities as: