# Cards marked with numbers 3, 4, 5, …...50 are placed in a box and mixed through. One card is drawn from the box. Find the probability that the number on the card is

(i) Divisible by 6

(ii) A single-digit number

Answer

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Hint: To solve the question, we have to calculate the number of possible outcomes at the given conditions. To calculate probability, divide the obtained number of outcomes to the total number of outcomes obtained when a card is drawn.

Complete step-by-step answer:

The numbers on the cards placed in a box given are 3, 4, 5, …...50

The number of possible outcomes when a card is drawn from the above-mentioned cards

= 50 – 2 = 48

Since, only 1, 2 numbers have not marked the cards considering the series of natural numbers.

The divisibility rule of 6 is that the number should be divisible by both numbers 2 and 3. The number is divisible by 2 if it is an even number. The number is divisible by 3 when the sum of all the digits of the number is a multiple of 3.

Since, the marked numbers are in the range of the first 10 multiples of 6. We have to list the multiples of 6 below 50. Thus, we get 6, 12, ,18, 24, 30, 36, 42, 48 are the multiples of 6 that are marked on the given cards.

Thus, the number of outcomes of getting a card marked number which is divisible by 6 when a card is drawn = 8.

The probability of getting a card marked number which is divisible by 6 when a card is drawn = Ratio of the number of outcomes of getting a card marked number which is divisible by 6 when a card is drawn to the number of possible outcomes when a card is drawn from the above-mentioned cards

\[=\dfrac{8}{48}\]

\[=\dfrac{1}{6}\]

\[\therefore \] The probability of getting a card marked number which is divisible by 6 when a card is drawn \[=\dfrac{1}{6}=0.16\]

3, 4, 5, 6, 7, 8, 9 are the single-digit numbers among the numbers marked on the cards when a card is drawn.

Thus, the number of outcomes of getting a single-digit number marked card when a card is drawn

= 7

The probability of getting a single-digit number marked card when a card is drawn = Ratio of the number of outcomes of getting a single-digit number marked card when a card is drawn, to the number of possible outcomes when a card is drawn from the above-mentioned cards

\[=\dfrac{7}{48}\]

\[\therefore \] The probability of getting a single-digit number marked card when a card is drawn \[=\dfrac{7}{48}=0.146\]

Note: The possibility of mistake can be not able to analyse the given condition independently and apply the quick method of calculating the number of outcomes instead of the general approach since the given marked numbers are below 50 which ease the calculation.

Complete step-by-step answer:

The numbers on the cards placed in a box given are 3, 4, 5, …...50

The number of possible outcomes when a card is drawn from the above-mentioned cards

= 50 – 2 = 48

Since, only 1, 2 numbers have not marked the cards considering the series of natural numbers.

The divisibility rule of 6 is that the number should be divisible by both numbers 2 and 3. The number is divisible by 2 if it is an even number. The number is divisible by 3 when the sum of all the digits of the number is a multiple of 3.

Since, the marked numbers are in the range of the first 10 multiples of 6. We have to list the multiples of 6 below 50. Thus, we get 6, 12, ,18, 24, 30, 36, 42, 48 are the multiples of 6 that are marked on the given cards.

Thus, the number of outcomes of getting a card marked number which is divisible by 6 when a card is drawn = 8.

The probability of getting a card marked number which is divisible by 6 when a card is drawn = Ratio of the number of outcomes of getting a card marked number which is divisible by 6 when a card is drawn to the number of possible outcomes when a card is drawn from the above-mentioned cards

\[=\dfrac{8}{48}\]

\[=\dfrac{1}{6}\]

\[\therefore \] The probability of getting a card marked number which is divisible by 6 when a card is drawn \[=\dfrac{1}{6}=0.16\]

3, 4, 5, 6, 7, 8, 9 are the single-digit numbers among the numbers marked on the cards when a card is drawn.

Thus, the number of outcomes of getting a single-digit number marked card when a card is drawn

= 7

The probability of getting a single-digit number marked card when a card is drawn = Ratio of the number of outcomes of getting a single-digit number marked card when a card is drawn, to the number of possible outcomes when a card is drawn from the above-mentioned cards

\[=\dfrac{7}{48}\]

\[\therefore \] The probability of getting a single-digit number marked card when a card is drawn \[=\dfrac{7}{48}=0.146\]

Note: The possibility of mistake can be not able to analyse the given condition independently and apply the quick method of calculating the number of outcomes instead of the general approach since the given marked numbers are below 50 which ease the calculation.

Last updated date: 22nd Sep 2023

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