Question 1_ The following table summarizes the number of students at Kiddies Headstart Preschool, categorized by the students’ gender and whether they belong to the infant or toddler section Infant Toddler Total Male 12 28 Female 34 26 Total 100 a) A student is selected at random. Find the probability that i. the student is male and a toddler ii. the student is female or an infant iii. the student is an infant, given that they are female. b) Are the events ‘Infant’ and ‘Female’ Mutually Exclusive? Justify your response c) Are the events ‘Infant’ and ‘Female’ Independent? Justify your response
Question 1_
The following table summarizes the number of students at Kiddies Headstart Preschool, categorized by the students’ gender and whether they belong to the infant or toddler section
|
|
Infant |
Toddler |
Total |
|
Male |
12 |
28 |
|
|
Female |
34 |
26 |
|
|
Total |
|
|
100 |
a) A student is selected at random. Find the probability that
i. the student is male and a toddler
ii. the student is female or an infant
iii. the student is an infant, given that they are female.
b) Are the
c) Are the events ‘Infant’ and ‘Female’ Independent? Justify your response
Question 2
The discrete probability distribution is given by
|
0 |
1 |
2 |
3 |
|
|
0 |
k |
2k |
3k |
i. Show that k = 1/6
ii. Find the mean of the probability distribution.
iii. Find the variance of the probability distribution.
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