Q65 of 66 Page 15

Peter throws two different dice together and finds the product of the two numbers obtained. Rina throws a die and squares the number obtained. Who has the better chance to get the number 25.[CBSE 2017]

Sample space when Peter throws two dice:

S1 = {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6),


(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6),


(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6),


(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6),


(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6),


(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}


Case when the product of the numbers obtained on the dice is 25: {(5,5)}


∴ Probability of getting number 25 = 1/36 = 0.02778


Sample space when Rina throws a die:


S1 = {1, 2, 3, 4, 5, 6}


Case when the square of the number obtained on the die is 25: {5}


∴ Probability of getting number 25 = 1/6 = 0.1667


Thus, Rina has a better chance than Peter to get number 25.

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A card is drawn at random from a well - shuffled deck of playing cards. Find the probability that the card drawn is

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(ii) a black king


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(iv) either a king a queen [CBSE 2015]

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A game of chance consists of spinning an arrow on a circular board, divided into 8 equal parts, which comes to rest pointing at one of the numbers 1, 2, 3, …, 8 (Fig. 9), which are equally likely outcomes. What is the probability that the arrow will point at (i) an odd number (ii) a number greater than 3 (iii) a number less than 9.

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A number x is selected at random from the numbers 1, 2, 3 and 4. Another number y is selected at random from the numbers 1, 4, 9 and 16. Find the probability that product of x and y is less than 16.[CBSE 2016]

 66

Two different dice are thrown together. Find the probability that the numbers obtained have

(i) even sum, and


(ii) even product.[CBSE 2017]