I need 27-32 Two dice, one green and one yellow, are rolled. in each of Exercise

Question

I need 27-32

Two dice, one green and one yellow, are rolled. in each of Exercises 27-32. find the conditional probability, and also say whether the indicated pair of events is independent. the sum is 5, given that the green one is not 1 and the yellow one is 1. That the sum is 6, given that the green one is either 1 or 3 and the yellow one is 1. the yellow one is 4, given that the green one is 4. the yellow one is 5, given that the sum is 6. the dice have the same parity, given that both of them are odd. the sum is 7, given that the dice do not have the same parity

Explanation / Answer

Dear Student Thank you for using Chegg !! Given that two dice (1 green and 1 yellow) are rolled 27) Probability that the sum is 5 given that green one is not 1 and yellow one is 1 Conditiona probability of even A given event B is P(A/B) = P (A & B) / P(B) P(A) = Number of ways to get sum 5 when two dice are rolled 1,4 2,3 3,2 4,1 => 4/36 P(B) = Probabilty that Green is not 1 and yellow is 1 2,1 3,1 4,1 5,1 6,1 = 5/36 P (A & B) / P(B) = 1/5 (Since only one of the case listed in P(B) is also available in P(A), therefore P(A&B) = 1 Solution Now since A&B is not a null set (In fact equal to (4,1)), therefore the two events are not independent As per Chegg guidelines an expert can answer maximum one question at a time.

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