Respuesta :
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:
[tex]\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}[/tex]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:
[tex]\begin{gathered} P(any\text{ number)= }\frac{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)= }\frac{1}{6}+\frac{1}{6}+\frac{1}{6}=\frac{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)= }\frac{1}{6}+\frac{1}{6}+\frac{1}{6}=\frac{3}{6} \\ \\ P(\text{at least 4 AND odd number) = }\frac{1}{6} \\ \\ \\ \therefore P(\text{at least 4 or odd number)=}\frac{3}{6}+\frac{3}{6}-\frac{1}{6}=\frac{5}{6} \end{gathered}[/tex]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:
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