Find the probability that a two-digit number | vedclass

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Question

(A) The total number of two-digit numbers that can be formed using the digits $\{1, 2, 3, 4, 5\}$ with repetition allowed is $5 	imes 5 = 25$.$A$ num

Vedclass · Accepted Answer

$\frac{1}{5}$

Vedclass · Answer

(A) The total number of two-digit numbers that can be formed using the digits $\{1, 2, 3, 4, 5\}$ with repetition allowed is $5 	imes 5 = 25$.$A$ number is divisible by $4$ if the number formed by its last two digits is divisible by $4$. For a two-digit number,the number itself must be divisible by $4$.The possible two-digit numbers formed by these digits are:$12, 16$ (not possible),$24, 32, 44, 52$.Checking divisibility by $4$:$12 \div 4 = 3$$24 \div 4 = 6$$32 \div 4 = 8$$44 \div 4 = 11$$52 \div 4 = 13$The favourable outcomes are $\{12, 24, 32, 44, 52\}$.Number of favourable outcomes $= 5$.Required probability $= \frac{	ext{Number of favourable outcomes}}{	ext{Total number of outcomes}} = \frac{5}{25} = \frac{1}{5}$.

Find the probability that a two-digit number formed by the digits $1, 2, 3, 4, 5$ is divisible by $4$ (repetition of digits is allowed).

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