2 When a fair dif is roiled once and the uppar face is observed, find the probabilitien of each of the following eventas

[13) A the event of “patims sn oven mumber”?
[2. B the event of “yatting an even number fess than or equal io 4”,
[a C the event of “getting a mumber that is not divisuble by 2”,
(4) D the event of "getting a number that in divinible by 7 ".
(5) [4] E the event of “getling a prime odd number”.
(B) 0.1 ) the event of "getting a number greater than 6 ",
(7) 14 G the event of “getting a number less than 8”.
(B) the event of "getting the number 4 ".
(a) I the event of “getting a perfect square number”.

10J J the event of "getting a number that satisfies the inequality : ",

Question

2 When a fair dif is roiled once and the uppar face is observed, find the probabilitien of each of the following eventas

[13) A the event of “patims sn oven mumber”?
[2. B the event of “yatting an even number fess than or equal io 4”,
[a C the event of “getting a mumber that is not divisuble by 2”,
(4) D the event of "getting a number that in divinible by 7 ".
(5) [4] E the event of “getling a prime odd number”.
(B) 0.1 ) the event of "getting a number greater than 6 ",
(7) 14 G the event of “getting a number less than 8”.
(B) the event of "getting the number 4 ".
(a) I the event of “getting a perfect square number”.

10J J the event of "getting a number that satisfies the inequality :

",

UpStudy AI · Accepted Answer

1) $$ A $$: Even numbers are $$2,\ 4,\ 6$$. There are 3 favorable outcomes, so  
$$
P(A)=\frac{3}{6}=\frac{1}{2}.
$$

2) $$ B $$: Even numbers less than or equal to 4 are $$2$$ and $$4$$. Thus,  
$$
P(B)=\frac{2}{6}=\frac{1}{3}.
$$

3) $$ C $$: Numbers not divisible by 2 (i.e. odd numbers) are $$1,\ 3,\ 5$$. Therefore,  
$$
P(C)=\frac{3}{6}=\frac{1}{2}.
$$

4) $$ D $$: No number on a six-faced die is divisible by 7, so  
$$
P(D)=0.
$$

5) $$ E $$: Prime odd numbers. Among $$1,\ 3,\ 5$$, note that $$1$$ is not prime, so only $$3$$ and $$5$$ qualify. Hence,  
$$
P(E)=\frac{2}{6}=\frac{1}{3}.
$$

6) $$ F $$: Numbers greater than 6 do not appear on a six-faced die, so  
$$
P(F)=0.
$$

7) $$ G $$: Numbers less than 8 include all outcomes $$1,\ 2,\ 3,\ 4,\ 5,\ 6$$. Thus,  
$$
P(G)=\frac{6}{6}=1.
$$

8) $$ H $$: The number 4 appears exactly once, therefore,  
$$
P(H)=\frac{1}{6}.
$$

9) $$ I $$: Perfect square numbers from the set are $$1$$ (since $$1^2=1$$) and $$4$$ (since $$2^2=4$$). So,  
$$
P(I)=\frac{2}{6}=\frac{1}{3}.
$$

10) $$ J $$: Numbers satisfying $$ x\geq 3 $$ are $$3,\ 4,\ 5,\ 6$$. Hence,  
$$
P(J)=\frac{4}{6}=\frac{2}{3}.
$$
1) $$ A $$: 0.5 2) $$ B $$: 0.333... 3) $$ C $$: 0.5 4) $$ D $$: 0 5) $$ E $$: 0.333... 6) $$ F $$: 0 7) $$ G $$: 1 8) $$ H $$: 0.166... 9) $$ I $$: 0.333... 10) $$ J $$: 0.666...

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