Answer :

Given that tickets are numbered from 1 to 10.

It is told that two tickets are drawn one after other in random.

We need to find the probability that number on ticket is a multiple of 5 and other number is multiple of 4.

Let us find the individual probabilities first

⇒ P(T_{51}) = P(Number on ticket is multiple of 5 in 1^{st} draw)

⇒

⇒

⇒

⇒ P(T_{41}) = P(Number on ticket is multiple of 4 in 1^{st} draw)

⇒

⇒

⇒

⇒ P(T_{52}) = P(Number on ticket is multiple of 5 in 2^{nd} draw)

⇒

⇒

⇒ P(T_{42}) = P(Number on ticket is multiple of 4 in 2^{nd} draw)

⇒

⇒

⇒ P(D_{54}) = P(Drawing one ticket which is multiple of 5 and other is multiple of 4)

⇒ P(D_{54}) = P(Drawing 5 multiple ticket first and 4 multiple ticket next) + (P(Drawing 4 multiple ticket first and 5 multiple ticket next)

Since drawing tickets are independent their probabilities multiply each other,

⇒ P(D_{54}) = (P(T_{51})P(T_{42})) + (P(T_{41})P(T_{52}))

⇒

⇒

⇒

∴ The required probability is .

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