The numbers 1 2 3 and 4 are written on slips of paper and 2

The numbers 1, 2, 3, and 4 are written on slips of paper, and 2 slips are drawn at random one at a time without replacement. Find the given probabilities.

a) The probability that the sum of the numbers is 7 is ______.

b) The probability that the sum of the numbers is 4 or less is _______.

c) The probability that the first number is 2 or the sum is 5 is _______.

Solution

Consider the table of results:

a)

There are 12 results. Two of them have a sum of 7.

Thus,

P(sum of 7) = 2/12 = 1/6 or 0.1666667 [answer]

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b)

Counting, 4 results have a sum of 4 or less.

Thus,

P(sum of 4 or less) = 4/12 = 1/3 or 0.3333333 [answer]

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c)

Counting,

P(first is 2) = 3/12 = 1/4 or 0.25
P(sum of5) = 4/12 = 1/3 or 0.33333333
P(first is 2 AND the sum is 5) = 1/12 = 0.083333

Thus,

P(first is 2 OR sum is 5) = P(first is 2) + P(sum is 5) - P(first is 2 AND the sum is 5)

= 1/4 + 1/3 - 1/12

= 1/2 or 0.5 [ANSWER]