The probability that a 4 is drawn from A followed by a 2 from B is 1/24
The probability of an event is defined as the possibility of an event occurring against sample space.
[tex]\large { \boxed {P(A) = \frac{\text{Number of Favorable Outcomes to A}}{\text {Total Number of Outcomes}} } }[/tex]
Permutation is the number of ways to arrange objects.
[tex]\large {\boxed {^nP_r = \frac{n!}{(n - r)!} } }[/tex]
Combination is the number of ways to select objects.
[tex]\large {\boxed {^nC_r = \frac{n!}{r! (n - r)!} } }[/tex]
Let us tackle the problem.
The probability of choosing a 4 ( 1 ball ) from Urn A is:
[tex]P(A) = \boxed{\frac{1}{6}}[/tex]
The probability of choosing a 2 ( 1 ball ) from Urn B is:
[tex]P(B) = \boxed {\frac{1}{4}}[/tex]
The probability that a 4 is drawn from A followed by a 2 from B is
[tex]P(A \cap B) = P(A) \times P(B)[/tex]
[tex]P(A \cap B) = \frac{1}{6} \times \frac{1}{4}[/tex]
[tex]P(A \cap B) = \boxed {\frac{1}{24}}[/tex]
Grade: High School
Subject: Mathematics
Chapter: Probability
Keywords: Probability , Sample , Space , Six , Dice , Die , Binomial , Distribution , Mean , Variance , Standard Deviation
