Answer:
[tex]\frac{1}{3}[/tex]
Step-by-step explanation:
In probability, "AND" means "MULTIPLICATION" and "OR" means "ADDITION".
Here we want "AND", so we need to multiply individual probability.
Probability of getting a 2 in first roll is 1/6 [one 2 and 6 numbers in total]
Also
Probability of getting a 4 in 2nd roll is 1/6 [one 4 and 6 numbers in total]
Hence, P (2 and 4) = 1/6 + 1/6 = 2/6 = 1/3
Answer: The required probability is [tex]\dfrac{1}{36}.[\tex]
Step-by-step explanation: Given that a dice is rolled twice.
We are to find the probability that we will get a 2 and a 4.
Let A and B denote the events of getting a 2 and a 4 respectively.
The sample space, S = {1, 2, 3, 4, 5, 6}
⇒ n(S) = 6.
Also, A = {2} ⇒ n(A) = 1 and B = {4} ⇒ n(B) = 1.
Then, the probabilities of events A and B are given by
[tex]P(A)=\dfrac{n(A)}{n(S)}=\dfrac{1}{6},\\\\\\P(B)=\dfrac{n(B)}{n(S)}=\dfrac{1}{6}.[/tex]
Since the events A and B are independent of each other, so the probability that we will get a 2 and a 4 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]
