Problem answering question 7 and 8. Suppose that a red jar has 34 amber, 15 gran

Question

Problem answering question 7 and 8.

Suppose that a red jar has 34 amber, 15 granite, and 27 quartz pebbles: a blue jar has 43 amber and 35 quartz pebbles: and a purple jar has 55 quartz and 11 granite pebbles. If someone takes one pebble at random out from each jar, what is the probability of drawing (a) two quartz and one amber pebbles? (b) all pebbles of quartz? (c) all pebbles of different kinds? Consider only the same blue and purple jars from problem #7. Suppose that now, a person picks jars and draws pebbles at random in the following sequence: 1. Pick any of the two jars. 2. Draw a pebble from the jar selected in step 1. 3. Pick any of the two jars again after mixing them and drop the pebble into that jar. 4. Mix the two jars and then pick any jar. 5. Stir the pebbles from the jar picked in step 4 and draw a pebble. (a) What is the probability that the jar picked in the fourth step has now three kinds of pebbles? (b) What is the probability that both pebbles drawn are amber?

Explanation / Answer

Problem 7:

The total number of each kind of pebbles in the three jars is recorded as:

a) Probability of drawing 2 quartz and one amber pebbles is computed as:

= P( Amber from red jar and quartz from other 2 jars ) + P( Amber from blue jar and quartz from other 2 jars )

= (34/76)*(35/78)*(55/66) + (27/76)*(43/78)*(55/66)

= 0.3305

Therefore 0.3305 is the required probability here.

b) Probability that all pebbles drawn are quartz

= (27/76)*(35/78)*(55/66) = 0.1328

Therefore 0.1328 is the required probability here.

c) Probability that all pebbles are different

= P( Amber from red jar, granite from purple and quartz from blue ) + P( amber from blue jar, granite from red and quartz from purple ) + P( amber from blue jar, granite from purple and quartz from blue )

= (34/76)*(11/66)*(35/78) + (43/78)*(15/76)*(55/66) + (43/78)*(27/76)*(11/66)

= 0.1568

Therefore 0.1568 is the required probability here.

Amber Granite Quartz Total Red Jar 34 15 27 76 Blue Jar 43 0 35 78 Purple Jar 0 11 55 66

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