 Hi friends I am Purva and today we will work out the following question. Cards marked with numbers 3, 4, 5 and so on up to 50 are placed in a box and mixed thoroughly. One card is drawn at random from the box. Find the probability that number on the drawn card is first divisible by 7, second a number which is a perfect square. Let us begin with the solution now. Now we are given that cards marked with numbers 3, 4, 5 and so on up to 50 are placed in a box and mixed thoroughly. So we have total number of cards is equal to 48. Because the card marked with number 3 is the first card, card marked with number 4 is the second card and so on the card marked with number 50 will be the 48 card. So we have total number of cards is equal to 48. Now we are given one card is drawn at random from the box and we have to find the probability that the number on the drawn card is in the first part we have to find divisible by 7. Now from 3 to 50 the numbers that are divisible by 7 are 7, 14, 21, 28, 35, 42 and 49. So number of favourable outcomes. Now the favourable outcomes are getting number 7, 14, 21, 28, 35, 42, 49 and this is equal to 7. That is the number of favourable outcomes are 7. That is from 3 to 50 these are the 7 numbers that are divisible by 7. Therefore probability of getting a number divisible by 7 is equal to 7 upon 48. Because total number of cards are 48 out of which cards marked with numbers 7, 14, 21, 28, 35, 42 and 49 are divisible by 7. And we know that for any event E probability of E is equal to number of outcomes favourable to E upon total number of outcomes. Now here event E is getting a number divisible by 7 and number of outcomes favourable to getting a number divisible by 7 are 7. And total number of outcomes that is total number of cards are 48. So we get probability of getting a number divisible by 7 is equal to 7 upon 48. Now in the second part we have to find the probability that number on the drawn card is a number which is a perfect square. Now from 3 to 50 the numbers with form of perfect square are 4, 9, 16, 25, 36 and 49. So number of favourable outcomes. Now the favourable outcomes are 4, 9, 16, 25, 36, 49 and these are 6 in number. So we get number of favourable outcomes are 6. Therefore probability of card having a number which is a perfect square is equal to 6 upon 48. Now again total number of cards are 48 out of which there are 6 cards marked with numbers 4, 9, 16, 25, 36 and 49 which form a perfect square. Now we know that for any event E probability of E is equal to number of outcomes favourable to E upon total number of outcomes. Now here event E is card has a number which is a perfect square and number of outcomes favourable to getting a card which is a perfect square are 6. And total number of cards that is total number of outcomes are 48. So probability of card having a number which is a perfect square is equal to 6 upon 48 and this is equal to 1 upon 8. This is our answer for the second part. So we have got the answer for the first part as 7 upon 48 and the answer for the second part as 1 upon 8. Hope you have understood the solution. Bye and take care.