A shoe box contains pieces of paper numbered 1through 15. Two pieces of paper ar

Question

A shoe box contains pieces of paper numbered 1through 15. Two pieces of paper are drawn, in succession,withoutreplacement. Find the probability of each of the following. a) Both numbers are odd. b) One number is even and the other number is odd. c) The first number is greater than 10 and the second numberis less than 5. A shoe box contains pieces of paper numbered 1through 15. Two pieces of paper are drawn, in succession,withoutreplacement. Find the probability of each of the following. a) Both numbers are odd. b) One number is even and the other number is odd. c) The first number is greater than 10 and the second numberis less than 5.

Explanation / Answer

A shoe box contains pieces of paper numbered 1through 15. Two pieces of paper are drawn, in succession,withoutreplacement. Find the probability of each of the following. a) Both numbers are odd. b) One number is even and the other number is odd. c) The first number is greater than 10 and the second numberis less than 5. : a) (8/15) (7/14) = (8/15) (1/2) = 8/30= 4/15
breakdown: 8 odds with 15 numbers.......once an odd is drawnthere is 7 odds left and only 14 numbers : b) (8/15) (7/14) + (7/15) (8/14) = (8/15) (1/2) + (7/15) (4/7)= (8/30) +(4/15)=(4/15)+(4/15) = 8/15    breakdown...there are two ways to get the evenand an odd..........1st pick even 2nd pick odd OR 1st pick oddand 2nd pick even...... the left side of the addition sign is the2nd scenario and the right side of the addition sign is the firstscenario remembering that the amount of evens or odds depending on thescenario decreases by one from first to second draw. the number oftotal numbers is also reduced by one : c)(5/15) (4/14) = (1/3) (2/7) = 2/21 :   breakdown....there are 5 numbers greater than 10out of 15 possibles on the first draw......once a draw is madethere is 14 numbers left.....and for the second draw there are 4numbers less than 5.

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