Question

A black and a red die are rolled together. Find the conditional probability of obtaining the sum 8 , given the red die resulted in a number less than 4. ..???

Answer 1

here is your answer Given one black die and one red die are rolled. The sample space of equally likely events = 6 ×× 6 = 36.

Let E: set of events where the sum is greater than 9. E: (6,4), (4,6), (5,5), (5,6), (6,5), (6,6). The total possible outcomes = 6.

⇒P(E)=Number of favorable outcomes in ETotal number of outcomes in S=636=16⇒P(E)=Number of favorable outcomes in ETotal number of outcomes in S=636=16

Let F be set of events where the black die rolled a 5. F: (1,5), (2,5), (3,5), (4,5), (5,5), (6,5). The total possible outcomes = 6.

⇒P(F)=Number of favorable outcomes in FTotal number of outcomes in S=636=16⇒P(F)=Number of favorable outcomes in FTotal number of outcomes in S=636=16

For our set of events $E \cap F =(5,5), (6,6). Total number of outcomes = 2.

⇒P(E∩F)=Number of favorable outcomesTotal number of outcomes in S=236⇒P(E∩F)=Number of favorable outcomesTotal number of outcomes in S=236.

Given P(E), P(F), P(E ∩∩ F), P(E/F) =P(E∩F)P(F)=P(E∩F)P(F)

⇒P(E/F)=23616⇒P(E/F)=23616 = 13I hope it's help you

Answer 2

Hey !!

A : Getting a sum of 8 , B : Red die resulted in no. < 4

 P (A/B) = P ( A ∩ B ) / P (B)

    = 2 / 36 / 18 / 36

      = 1 / 9

Good luck !!