10 different names are put into the computer and one of the name is Colin. a) On Saturday, the computer chooses 2 names at random. The computer is set so the same name *can* be chosen twice. What is the probability that Colin is chosen at least once? b) On Sunday, the computer is set so that the same name *cannot* be chosen twice. Work out the probability that Colin is chosen.

a. The Probability that his name will be selected AT LEAST ONCE (with replacement) = 19/100

b. The probability of selecting Colin's name (without replacement)

= 1/5

Step-by-step explanation:

If a name can be selected twice by the computer with replacement, then the probability that Colin's name will be selected at least once is - the probability that his name will be selected in the first attempt or that his name will be selected in the second attempt or that his name will be selected in both attempts.

Since Colin is just one out of ten names that are put into the computer, he has one chance out of ten to be selected and other names are seen as having a combined 9/10 chance.

a. The probability that Colin's name will be selected at the first attempt is:

P(first attempt) (with replacement)

(1/10) × 9/10

= 9/100

His name can also be selected in the second attempt.

P(second attempt)

= (9/10) × 1/10

= 9/100

He can also be selected in both attempts.

P(both attempt)

= (1/0) × 1/10

= 1/100

The probability that his name will be selected at least once = (9/100) + (9/100) + (1/100)

= 19/100

ALTERNATIVELY

The probability that Colin's name will be selected at least once can be calculated by subtracting the probability of not selecting Colin from 1.

That is, 1- P (not selecting Colin's name)

P(not selecting colin) =

9/10 × 9/10

= 81/100

1 - P(not selecting Colin's name)

1- (81/100)

= 19/100

b. The probability of selecting Colin in two attempts without replacement is:

1 - P (not selected)

= (9/10) × 8/9

= 8/10

Subtracting this probability from 1 will then give:-

1 - (8/10)

= 2/10

= 1/5

Therefore the probability of selecting colin with replacement is 19/100 and the probability of selecting him without replacement is 1/5

1,8,15,22,29,36,43,50

step-by-step explanation: