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a coin and a die are thrown. find the probability of getting

a head or an even numbr

a tail or an odd numbr

$G i v e n, a c o i n a n d a d i e a r e t h r o w n . S o, T o t a l n u m b e r o f o u t c o m e s n (S) = 2 \times 6 = 12 (1) L e t E b e t h e e v e n t o f a h e a d o r a n e v e n n u m b e r . S o, E = {(H, 2), (H, 4), (H, 6)} \Rightarrow n (E) = 3 T h u s, P (a h e a d o r a n e v e n n u m b e r) = \frac{n (E)}{n (s)} \Rightarrow P (a h e a d o r a n e v e n n u m b e r) = \frac{3}{12} = \frac{1}{4} (2) L e t F b e t h e e v e n t o f a t a i l o r a n o d d n u m b e r . S o, F = {(T, 1), (T, 3), (T, 5)} \Rightarrow n (F) = 3 T h u s, P (a t a i l o r a n o d d n u m b e r) = \frac{n (F)}{n (s)} \Rightarrow P (a t a i l o r a n o d d n u m b e r) = \frac{3}{12} = \frac{1}{4}$

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