Question

A box contains 17 balls numbered 1 through 17. Two balls are drawn in succession without replacement. If the second ball has the number 4 on it, what is the probability that the first ball had a smaller number on it? An even number on it?

Answer 1

1 ; 7 /17

Explanation:

17 balls numbered 1 through 17

Picking without replacement :

If the second ball picked = 4

P(first ball has a smaller number)

Numbers less Than = (3, 2, 1)

P(number less than second ball Given 4 is drawn for second ball) :

= (3/17 * 1/16) ÷ (3/17 * 1/16) +) 14/17 * 0)

= (3 / 272) / (3 /272) * 0

= 3 / 272 * 272 / 3

= 1

2.)

(8/17 * 7/8) ÷ (8/17 * 7/8) + (9/17 * 1/17)

7/17 ÷ (7 /17) + 10/17

7 /17 ÷ 17/17

7/17 ÷ 1

7 /17