An urn contains 8 red chips and 4 blue chips. Two chips are selected one at a time and without replacement (wtr). (2)a. Use FPC to determine the number of ways a red chip and a blue chip (not necessarily in that order) can be selected.b. Find the probability of selecting a red chip and a blue chip.

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Asked Sep 13, 2019
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An urn contains 8 red chips and 4 blue chips. Two chips are selected one at a time and without replacement (wtr). (2)
a. Use FPC to determine the number of ways a red chip and a blue chip (not necessarily in that order) can be selected.
b. Find the probability of selecting a red chip and a blue chip.

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Expert Answer

Step 1

FPC here refers to the Fundamental Principle of Counting which states that if there are m outcomes for an event A and n outcomes for an event B, then the number of outcomes for event A and B combined would be m*n 

a) m * n = 32

Number of ways a red chip
can be selected (m) C
can be selected (n) C
Number of ways a blue chip
Ways in which a red chip and a blue chip can be selected one at a time (m x n) C * C*
= 32
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Number of ways a red chip can be selected (m) C can be selected (n) C Number of ways a blue chip Ways in which a red chip and a blue chip can be selected one at a time (m x n) C * C* = 32

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Step 2

b) probability of selecting a red chip and...

Ways in which a red chip and a blue chip can be selected one at a time CC
=32
Total number of ways in which 2 chips can be drawn from the entire sample-C *C
Favorable ways
Probability of drawing 1 red chip and 1 blue chip
Total number of ways
33
0.24242
help_outline

Image Transcriptionclose

Ways in which a red chip and a blue chip can be selected one at a time CC =32 Total number of ways in which 2 chips can be drawn from the entire sample-C *C Favorable ways Probability of drawing 1 red chip and 1 blue chip Total number of ways 33 0.24242

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