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➷There is a dice and you have 6 numbers
The probability is 1/36, since it is 1/6 to get a 2 the first time, and 1/6 to get a 1 the next time.
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DOGE
Answer: The required probability is [tex]\dfrac{1}{36}.[/tex]
Step-by-step explanation: We are given that a six-sided number cube is rolled.
We are to find the probability of getting a 2 and then a 1, given that the first number rolled was 2.
Let S denotes the sample space of rolling a six-sided cube, A be the event of rolling a 2 and B be the event of rolling a 1.
Then,
n(S) = 6, n(A) = 1 and n(B) = 1.
Now, the probabilities of events A and B :
[tex]P(A)=\dfrac{n(A)}{n(S)}=\dfrac{1}{6},\\\\\\P(B)=\dfrac{n(B)}{n(S)}=\dfrac{1}{6}.[/tex]
Since the two events A and B are independent of each other, so the required probability is given by
[tex]P(A\cap B)=P(A)\times P(B)=\dfrac{1}{6}\times\dfrac{1}{6}=\dfrac{1}{36}.[/tex]
Thus, the required probability is [tex]\dfrac{1}{36}.[/tex]
