Question

An unbiased coin is tossed. If the outcome is a head then a pair of unbiased dice is rolled and the sum of the numbers obtained on them is noted. If the toss of the coin results in tail then a card from a well-shuffled pack of nine cards numbered 1,2,3,..,9 is randomly picked and the number on the card is noted. The probability that the noted number is either 7 or 8 is?

Answer 1

Answer:

19/72

Step-by-step explanation:

P(h) p (7 or 8) + p(t)p(7 or 8) (head then sum on dice 7 or 8, tell then number on ticket 7 or 8 )

=1 /2× 11 /36 + 1/ 2 × 2/9 = 19/72

Answer 2

Answer:

      19 / 72

Step-by-step explanation:

By the Law of Total Probability...

  P(7 or 8)

= P(7 or 8 | head) × P(head)  +  P(7 or 8 | tail) × P(tail)

= P(7 or 8 on dice) × (1/2)  +  P(7 or 8 from cards) × (1/2)

= (11/36) × (1/2)  +  (2/9) × (1/2)

= 11/72  +  1/9

= 11/72  +  8/72

= 19/72

Note:  For P(7 or 8 on dice), there are 36 possible outcomes with two dice, and 11 favourable outcomes:  (1,6), (2,5), (3,4), (4,3), (5,2), (6,1), (2,6), (3,5), (4,4), (5,3), (6,2).  So the probability is 11/36.