Probability 3 Question 5

5. 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

(a) 1572

(b) 1336

(c) 1972

(d) 1936

(2019 Main, 10 Jan I)

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Solution:

  1. Clearly, P(H)= Probability of getting head =12

 and P(T)= Probability of getting tail =12

Now, let E1 be the event of getting a sum 7 or 8 , when a pair of dice is rolled.

Then, $E _1={(6,1),(5,2),(4,3),(3,4),(2,5)$,

Extra close brace or missing open brace

P(E1)= Probability of getting 7 or 8 when a pair of dice is thrown =1136

Also, let P(E2)= Probability of getting 7 or 8 when a card is picked from cards numbered 1,2,.,9=29

Probability that the noted number is 7 or 8

=P((HE1) or (TE2))=P(HE1)+P(TE2)

[(HE1) and (TE2) are mutually exclusive] =P(H)P(E1)+P(T)P(E2)

[H,E1 and T,E2 both are sets of =12×1136+12×29=1972 independent events]



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