1. You have 25 keys on a key chain one at a time trying to open the lock. Assume

Question

1. You have 25 keys on a key chain one at a time trying to open the lock. Assume that 24 keys will not unluck, while 1 key will unlock! What is the probability that the rst key you select opens the lock? The second key (which would mean the rst didn’t work)? The third key?..The last key (i.e., the rst 24 do not work!)?

2. An Urn contains 4 Red and 6 Black balls and a second Urn contains 16 Red and an unknown number of black balls. A single ball is drawn from each urn and it is known that the probability that both balls are the same color is .44. Determine the number of black balls in the second Urn

3. Consider the following dice problems.

(a) Roll one die four times (or four dice once). Determine the probability of getting at least one 6 in the four rolls. (b) Roll two dice twenty-four times. Determine the probability of getting at least one double sixes in the twenty-four rolls.

Explanation / Answer

probabilty that first key will work =1/25

probability that secon key will work =P(first will not work *second will work) =(24/25)*(1/24)=1/25

probability that third key will work =P(first and second will not work *third will work) =(24/25)*(23/24)*(1/23)=1/25

similarly that last key will work=1/25

2)let there are x black balls in urn 2

hence probabilty of both balls of same color =P(both red+both black)

=(4/10)*(16/(16+x))+(6/10)*(x/((16+x)) =0.44

64+6x =70.4+4.4x

1.6x=6.4

x=4

3) probability of getting at least one 6 in the four rolls =1-P(none of four rolls show a four)=1-(3/4)4 =0.6836

b)probability of getting at least one double sixes in the twenty-four rolls =1-P(none double sixes in 24 rolls)

=1-(35/36)24=0.4914

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