# Tickets are numbered from 1 to 10. Two tickets are drawn one after the other at random. Find the probability that the number on one of the tickets is a multiple of 5 and on the other a multiple of 4.

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(T51) = P(Number on ticket is multiple of 5 in 1st draw)

P(T41) = P(Number on ticket is multiple of 4 in 1st draw)

P(T52) = P(Number on ticket is multiple of 5 in 2nd draw)

P(T42) = P(Number on ticket is multiple of 4 in 2nd draw)

P(D54) = P(Drawing one ticket which is multiple of 5 and other is multiple of 4)

P(D54) = 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(D54) = (P(T51)P(T42)) + (P(T41)P(T52))

The required probability is .

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