the sum of two digits of a two digit number is 11 find the probability that the number is a 1. prime number 2. either divisible by 2 or 3

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Solution

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$T w o d i g i t n u m b e r s, t h e s u m o f w h o s e d i g i t s i s 11 : 29, 92, 83, 38, 74, 47, 56, 65 T o t a l n u m b e r s = 8 (i) P r o b a b i l i t y t h a t t h e n u m b e r i s a p r i m e n u m b e r : N u m b e r o f f a v o u r a b l e o u t c o m e s = N u m b e r o f p r i m e n u m b e r s = 3 {29, 47, 83} P r o b a b i l i t y = \frac{F a v o u r a b l e o u t c o m e s}{T o t a l o u t c o m e s} = \frac{3}{8} (i i) P r o b a b i l i t y t h a t t h e n u m b e r i s e i t h e r d i v i s i b l e b y 2 o r 3 : N u m b e r o f f a v o u r a b l e o u t c o m e s = N u m b e r o f n u m b e r s d i v i s i b l e b y 2 o r 3 = 4 {92, 38, 74, 56} P r o b a b i l i t y = \frac{F a v o u r a b l e o u t c o m e s}{T o t a l o u t c o m e s} = \frac{4}{8} = \frac{1}{2}$

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