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Determine the probability p, for each of the following events.

(a) An odd number appears in a single toss of a fair die.

(b) At least one head appears in two tosses of a fair coin.

(c) A king, 9 of hearts, or 3 of spades appears in drawing a single card from a well shuffled ordinary deck of 52 cards.

(d) The sum of 6 appears in a single toss of a pair of fair dice.

0 4 Views | Posted 3 months ago
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    Answered by

    Payal Gupta | Contributor-Level 10

    3 months ago

    This is a long answer type question as classified in NCERT Exemplar

    (a)  Possible  outcome  of  a  single  throw  of  die                 S = { 1 , 2 , 3 , 4 , 5 , 6 }     o u t     o f     w h i c h     1 , 3 , 5     a r e     o d d ∴           R e q u i r e d     p r o b a b i l i t y = 3 6 = 1 2 ( b )     W h e n     a     f a i r     c o i n     i s     t o s s e d     t w i c e ,     t h e n     t h e     s a m p l e     s p a c e                 S = { H H , H T , T H , T T } ∴           P r o b a b i l i t y     o f     g e t t i n g     a t l e a s t     o n e     h e a d ( H H , H T , T H ) = 3 4 ( c )     F a v o u r a b l e     e v e n t s     a r e     4     k i n g s + 2     o f     h e a r t s + 3     o f     s p a d e s = 4 + 1 + 1 = 6 = 6 5 2 = 3 2 6 ( d )     W h e n     a     p a i r     o f     d i c e     i s     r o l l e d ,     t h e n     t o t a l     n u m b e r     o f     s a m p l e     s p a c e = 3 6     o u t     o f     w h i c h                 ( 1 , 5 ) , ( 5 , 1 ) , ( 2 , 4 ) , ( 4 , 2 )     a n d     ( 3 , 3 )     a r e     t h e     f a v o u r a b l e     e v e n t s ∴             R e q u i r e d     p r o b a b i l i t y = 5 3 6 .

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