Can someon explain this in detail coz i do not understand it

Can someon explain this in detail coz i do not understand it how we get the numbers ?

For this Qa how we get the set of (1/6,1/6,1/6.....) and indeed with 5/6?

A die is biased (or loaded) no that 3 appears twice as often as each other number but that the other five outcomes are equally likely P(1) = P(2) = P(4) = P(5) = P(6) = 1/7 delta P(3) = 2/7 what is the prob of an odd number = 1/7 + 2/7 + 1/7 = 4/7 In rolling a die E is defined as the event representing an even no. & E_2 as the event representing a three or less than 3. What is P(E_1 Union E_2)? E_1 = {2, 4, 6} E_2 = {1, 2, 3} E_1 union E_2 =)1, 2, 3, 4, 6} E_1 intersection E_2 = {2} P(E_1 union E_2) = P(E_1) + P(E_2) - P(E_1 intersection E_2) = {1/6 + 1/6 + 1/6} + {1/6 + 1/6 + 1/6} - {1/6} = 5/6.

Solution

Dear Student Thank you for using Chegg !! Problem 1:- As given in the question that the face 3 of the dice is loaded twice as compared to rest of the faces Let the occurrence of rest of the equally likely faces be given by x Then occurrence of 3 will be given by 2x Since there are 6 faces of the dice we get the sample space as = 1 2 3 4 5 6 x x 2x x x x = 7x Now we need the probability of occurrence of odd face i.e. probability of occurrence of 1,3,5 Favourable outcomes are 1 3 5 x 2x x = 4x Probability = No of favourable outcomes / Sample space = 4x / 7x = 4/7 Ps:- Kindly note that at chegg we have a policy of answering 1 question at a time. Thnak you