1(i) using either an intuitive arguement or the muliplicationrule, decide whethe
ID: 2916558 • Letter: 1
Question
1(i) using either an intuitive arguement or the muliplicationrule, decide whether the following pairs of event are independent.where possible, draw a picture or a venn diagram. (a) Let Z have the standard Normal distribution: i A = [Z > 1] and B[Z < 2]. ii A = [-2 < Z < 2 ] and B = [Z > 0]. (b) A whole number b/w 1 and 20 is chosen at random. A = [Thenumber is even] and B = [The number is at most 6 ]. 1ii. The Harrison have decide to have children andwill shop when they have a child of each gender or when they havethree. Let Y be the number of girls theHarrison will have. (a) List the sample space and draw a tree diagram. (b) Draw a venn diagram of the event A = [The Harrisonshave at least one girl ] (c) Let B = [The Harrison have two children ] and C = [The Harrison sons have two sons.] (d) Use a tree diagram to find the probabilities of theevents A, B, and C pertaining the children theHarrison will have. 1(i) using either an intuitive arguement or the muliplicationrule, decide whether the following pairs of event are independent.where possible, draw a picture or a venn diagram. (a) Let Z have the standard Normal distribution: i A = [Z > 1] and B[Z < 2]. ii A = [-2 < Z < 2 ] and B = [Z > 0]. (b) A whole number b/w 1 and 20 is chosen at random. A = [Thenumber is even] and B = [The number is at most 6 ]. 1ii. The Harrison have decide to have children andwill shop when they have a child of each gender or when they havethree. Let Y be the number of girls theHarrison will have. (a) List the sample space and draw a tree diagram. (b) Draw a venn diagram of the event A = [The Harrisonshave at least one girl ] (c) Let B = [The Harrison have two children ] and C = [The Harrison sons have two sons.] (d) Use a tree diagram to find the probabilities of theevents A, B, and C pertaining the children theHarrison will have.Explanation / Answer
Cramster Rules: One question with related subparts perpost.1(i) using either an intuitive arguement or the muliplication rule,decide whether the following pairs of event are independent. wherepossible, draw a picture or a venn diagram. (a) Let Z have thestandard Normal distribution: i A = [Z > 1] and B[Z < 2]. ii A = [-2 < Z < 2 ] and B = [Z > 0 ]. (b) A whole number b/w 1 and 20 is chosen at random. A = [Thenumber is even] and B = [The number is at most 6 ].
P(A) = 10/20 = .50 P(B) = 6/20= .30 P(A and B) = 3/20 = .15
Since P(A)P(B) = P(A and B) the twoevents are independent.
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