Problem 1: Consider rolling a 6-sided die twice, where each one of the 36 possib
ID: 3202618 • Letter: P
Question
Problem 1: Consider rolling a 6-sided die twice, where each one of the 36 possible outcomes is equally likely to occur. Let A be the event that the first number thrown is no larger than 3, and let B be the event that the sum of the two numbers thrown. Find the sample space of A and the sample space B, then find the most probable values to occur in B.
Problem 2: How many possible ways can we arrange
a. 5 couples (10 people) sit in a row if every person has to sit next to his/her partner?
b. 9 women and 10 men sit around a round table if no two women sit together?
Explanation / Answer
Problem 1 :
Event A; The first number thrown is no larger than 3.
Sample space for event "A" is : 1,2, and 3 : (1,2,3)
And Event B : Sum of the two numbers thrown (Assuming that event "A" has occured; means first throw resulted in either 1,2,or 3 )
The following table is the sample space for "B" :
the most probable values to occur in B : 4 , 5, 6 and 7;
Number on Dice1 Number on Dice 2 Sum of two numbers 1 1 2 1 2 3 1 3 4 1 4 5 1 5 6 1 6 7 2 1 3 2 2 4 2 3 5 2 4 6 2 5 7 2 6 8 3 1 4 3 2 5 3 3 6 3 4 7 3 5 8 3 6 9