Cards marked with numbers 3,4,5, ...........,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 divisible by 7.

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\frac{1}{48}

\frac{7}{48}

\frac{7}{46}

\frac{5}{48}

answer is B.

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Detailed Solution

Given, cards marked with numbers 3,4,5, ..........., 50.
The P(A) of the random experiment as,

P (A) = \frac{Number of favorable outcomes}{Total number of outcomes}

The total number of outcomes in a deck marked with numbers are, 50 – 2 = 48.
The Events getting cards which has the number divisible by 7 are

\Rightarrow

n(X) = {7,14,21,28,35,42,49}

\Rightarrow

n(X)=7
So, the probability of getting cards which has the number divisible by 7 is,

P (E) = \frac{n (X)}{n (S)}

\Rightarrow P (E) = \frac{7}{48}

The probability of getting cards which has the number divisible by 7 is

\frac{7}{48}

.
Hence, option 2 is the correct answer.

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