One ticket is selected at random from $$100$$ tickets numbered $$00$$,$$01$$,$$02$$,…,$$99$$. Suppose A and B are the sum and product of the digit found on the ticket, respectively. Then $$P((A=7)/(B=0))$$ is given by

Question

One ticket is selected at random from $$100$$ tickets numbered $$00$$,$$01$$,$$02$$,…,$$99$$. Suppose A and B are the sum and product of the digit found on the ticket, respectively. Then $$P((A=7)/(B=0))$$ is given by

Infinity Learn · Accepted Answer

The sum of the digits can be $$7$$ in the following ways : $$07$$, $$16$$, $$25$$, $$34$$, $$43$$, $$52$$, $$61$$, $$70$$.∴ (A=7)={07$$,$$16$$,$$25$$,$$34$$,$$43$$,$$52$$,$$61$$,$$70}Similarly$$,$$(B=0)={00$$,$$01$$,$$02$$,…,$$10$$,$$20$$,$$30$$,…,$$90}Thus$$,$$(A=7)∩(B=0)={09$$,$$70}$$∴ $$P((A=7)∩(B=0))=2100$$,$$P((B=0))=19100Hence$$,$$P(A=7$$∣$$B=0)=P((A=7)∩$$(B=0))P(B=0)=210019100=219$$

One ticket is selected at random from 100 tickets numbered $00, 01, 02, \dots, 99$ . Suppose A and B are the sum and product of the digit found on the ticket, respectively. Then $P ((A = 7) / (B = 0))$ is given by

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One ticket is selected at random from 100 tickets numbered 00,01,02,…,99. Suppose A and B are the sum and product of the digit found on the ticket, respectively. Then P((A=7)/(B=0)) is given by

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One ticket is selected at random from 100 tickets numbered $00, 01, 02, \dots, 99$ . Suppose A and B are the sum and product of the digit found on the ticket, respectively. Then $P ((A = 7) / (B = 0))$ is given by