Q) 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 a 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) 13/36       b) 15/72           c) 19/36        d) 19/72

Ans:

Step 1: When we toss a coin, total number of outcomes = 2

Chance to get a head (or tail) = 1

∴ Probability to get a head (or tail) =

Step 2: Next, let’s start from dice (which is rolled after head):

We know that total number of possible combinations in case of pair of dice = 6 x 6 = 36

Next, Possible combinations to get 7: (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1)  = 6

Possible combinations to get 8: (2, 6), (3, 5), (4, 4), (5, 3), (6, 2) = 5

∴ Total number of possible combinations: 6 + 5 = 11

Hence probability to get 11=

∴ Probability to get 7 or 8 on dice =

Step 3: Next, let’s take deck of cards numbered from 1 to 9 (which are drawn after tail):

Total number of chances to draw a number from 1 to 9 = 9

Number of chances to get 7 or 8 from a deck of 9 cards = 2

Hence probability to get 11 =

∴ Probability to get 7 or 8 on cards =

Step 4: Probability to get 7 or 8 on dice or cards

= Probability to get 7 or 8 on dice + Probability to get 7 or 8 on cards

=

Since the probability of getting 7 or 8 is , hence option d) is correct.

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