Six different numbers are chosen at random from the set {1,2,3, … ,50}. a) What is...

Six different numbers are chosen at random from the set {1,2,3, … ,50}. a) What is the probability that a number greater than 40 is selected? b) What is the probability that a number greater than 40 is selected and

a number less than 10 is selected?

Solutions

Expert Solution

6 different numbers are selected randomly from the set {1,2,3....,50} . And it can be done so in ways = 15890700 ways

a) What is the probability that a number greater than 40 is selected?

Numbers greater than 40 are {41,42,43,...,50} i.e. 10 in numerical count. One number is selected from this group while the rest five are selected from the group {1,2,3,...40} which has a numerical count of 40.

This selection can be done in ways = 6580080 ways

Probability that a number greater than 40 is selected = Favorable events/Total events = 6580080/15890700 = 0.4141

b) What is the probability that a number greater than 40 and a number less than 10 is selected?

Numbers greater than 40 are {41,42,43,...,50} i.e. 10 in numerical count. One number is selected from this group. Another number is selected from the group {1,2,3,..10} which has a numerical count of 10 while the rest four are selected from the group {11,12,13,...40} which has a numerical count of 30.

This selection can be done in ways = 2740500 ways

Probability that a number greater than 40 and a number less than 10 is selected =

=Favorable events/Total events = 2740500/15890700=0.1725

Colby Messinger answered 1 year ago

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