The probability that if we will roll a 4, then rolling next a number less than 3 is given by: Option D: 1/18
What is the chain rule in probability for two events?
For two events A and B:
The chain rule states that the probability that A and B both occur is given by:
[tex]P(A \cap B) = P(A)P(B|A) = P(B)P( A|B)[/tex]
Which pair of events are called independent events?
When one event's occurrence or non-occurrence doesn't affect occurrence or non-occurrence of other event, then such events are called independent events.
Symbolically, we have:
Two events A and B are said to be independent iff we have:
[tex]P(A \cap B) = P(A)P(B)[/tex]
- For this case, let we define two events:
A = event of rolling a 4 in first roll - B = event of rolling a number less than 3 in second roll
Then A and B are independent as their outcomes are not directly related or prone to affect each other assumingly.
Thus, probability of rolling a 4, then rolling a number less than 3 is:
[tex]P(A \cap B) = P(A)P(B)[/tex]
Total number of outcomes for any roll = n(S) = 6
Favorable number of outcomes for event A = n(A) = 1 (since a 4 can occur in 1 way out of 6 results)
Thus, P(A) = n(A)/n(S) = 1/6
And, favorable number of outcomes for event B = n(B) = 2 (since numbers less than 3 are only 1 and 2, so two outcomes possible)
Thus, P(B) = n(B)/n(S) = 2/6
Hence, probability of rolling a 4, then rolling a number less than 3 is:
[tex]P(A \cap B) = P(A)P(B) = \dfrac{1}{6} \times \dfrac{2}{6} = \dfrac{2}{36} = \dfrac{1}{18}[/tex]
Therefore, the probability that if we will roll a 4, then rolling next a number less than 3 is given by: Option D: 1/18
Learn more about probability here:
brainly.com/question/1210781
