Question #11124

Ten cards numbered 1 to 10 are mixed in a hat.Two cards numbered p and q are drawn from the hat.What is the probability that p+q=10?

a) 2/5

b) 4/9

c) 7/45

d) 4/45

a) 2/5

b) 4/9

c) 7/45

d) 4/45

Expert's answer

a) 2/5b) 4/9

c) 7/45

d) 4/45

Solution.

The total number of all pairs (p,q) from numbers 1..10 is equal to

10 * (10-1) / 2 = 45

Notice that only the following 4 pairs (p,q) has property p+q=10:

1,9

2,8

3,7

4,6

Hence the probability that p+q=10 is equal to

4/45

Answer: d) 4/45

c) 7/45

d) 4/45

Solution.

The total number of all pairs (p,q) from numbers 1..10 is equal to

10 * (10-1) / 2 = 45

Notice that only the following 4 pairs (p,q) has property p+q=10:

1,9

2,8

3,7

4,6

Hence the probability that p+q=10 is equal to

4/45

Answer: d) 4/45

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