David Mash Icy teaches two undergraduate statistics. Courses at Kansas College.

Question

David Mash Icy teaches two undergraduate statistics. Courses at Kansas College. The class for Statistics 201 consists of 7 sophomores and 3 juniors. The mote advanced course. Statistics 301. has 2 sophomores and 8 juniors enrolled. As an example of a business sampling technique. Professor Mashley randomly selects, from the slack of Statistics 201 registration cards, the class card of one student anti then places that card hack in the stack. If that student was a sophomore. Mashley draws another card from the Statistics 201 stack, if not. he randomly draws a card from the Statistics 301 group. Arc these two draws independent events? What is the probability of a sophomore's name on both draws? a junior's name on both draw s? one sophomore's name and one junior's name on the two draws, regardless of order drawn?

Explanation / Answer

a) First draw is frrom Stat 201,

So, P (Junior on first draw) = 3 / 10 = 0.3

b)

If first card is a sophomore., the professor again draws from STAT 201

Since, it is sampling with replacement,

the probability of junior on second draw = 3 / 10 = 0.30

c)

If there is a juniors name on first draw, the professor will choose from STAT 301

P (Junior in 2nd draw) = 8/10 = 0.8

d)

Sophomore's name on both draws indicate both are taken from STAT 201

Thus,

required probability = 0.7 * 0.7

= 0.49

e)

Junior's name on both draws implies first one is from STAT 201 and next from STAT 301

thus, required probability = 0.3 * 0.8

= 0.24

f)

P ( One sophomore , one junior)

= (0.7 * 0.3) + (0.3 * 0.2)

= 0.27

Hope this helps.

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