Question

A bag contains cards from 2 to 90. A card is drawn at random from the bag. Find the proablity

Answer 1

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A bag contains cards which are numbered form 2 to 90. A card is drawn at random from the bag. Find the probability that it bears

(i)a two digit number

(ii)a number which is a perfect square.

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1) 81/89

2) 8/89

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★Given :-

Cards marked with numbers from 2 to 90

Total number of outcomes = 90 - 2 + 1 =  89 ( both 2 & 90 are included)

★(i)Let E1 = Event of getting a two digit number

Numbers which are 2 digits are from 10 to 90 = 90 - 10 + 1 = 81 ( both 10 & 90 are included)

Number of outcome favourable to E1 = 81

Probability (E1) = Number of favourable outcomes / Total number of outcomes

P(E1) = 81/89

Hence, the required probability of getting two digit number, P(E1) = 81/89  .

★(ii)Let E2 = Event of getting a number which are perfect squares  

Numbers which are perfect squares = 4, 9, 16, 25 ,35,49,64, 81

Number of perfect squares = 8  

Number of outcome favourable to E2 = 8

Probability (E2) = Number of favourable outcomes / Total number of outcomes

P(E2) = 8/89  

Hence, the required probability of getting a number which are perfect squares ,P(E2) = 8/89 .

Answer 2

Answer:-

Cards marked with numbers from 2 to 90

Total number of outcomes = 90 - 2 + 1 = 89 ( both 2 & 90 are included)

★(i)Let E1 = Event of getting a two digit number

Numbers which are 2 digits are from 10 to 90 = 90 - 10 + 1 = 81 ( both 10 & 90 are included)

Number of outcome favourable to E1 = 81

Probability (E1) = Number of favourable outcomes / Total number of outcomes

P(E1) = 81/89

Hence, the required probability of getting two digit number, P(E1) = 81/89 .

★(ii)Let E2 = Event of getting a number which are perfect squares

Numbers which are perfect squares = 4, 9, 16, 25 ,35,49,64, 81

Number of perfect squares = 8

Number of outcome favourable to E2 = 8

Probability (E2) = Number of favourable outcomes / Total number of outcomes

P(E2) = 8/89

Hence, the required probability of getting a number which are perfect squares ,P(E2) = 8/89 .