## Question

Two dice are rolled one after the other. The probability that the number on the first is smaller than the number on the second is:

### Solution

5/12

Two throws independent

So *P*(no. on *D*_{1} < no. on *D*_{2}) = *P*(no. on *D*_{2} < no. on *D*_{1})

⇒ Let *E*_{1} = Number on *D*_{1} < *D*_{2 }

*E*_{2} = Number on *D*_{2} < *D*_{1}

*F* = Number on *D*_{2} < *D*_{1 }

⇒ Let (*E*_{1}) + *P*(*E*_{2}) + *P*(*F*) = 1

⇒ 2*P*(*E*_{1}) + *P*(*F*) = 1…….(i)

*P*(*F*) = *P*(1) *P*(1) + *P*(2) *P*(2) +….+ *P*(6) *P*(6)

#### SIMILAR QUESTIONS

If A_{1}, A_{2},….A* _{n}* are any

*n*events, then

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An integer is chosen at random from the first 200 positive integers. The probability that the integer chosen is divisible by 6 or 8 is:

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If two events A and B are such that

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A box contain 100 tickets numbered 1, 2,…100. Two tickets are chosen at random. It is given that the greater number on the two chosen tickets is not more than 10. The probability that the smaller number is 5 is:

A bag contains four tickets marked with numbers 112, 121, 211, 222. One ticket is drawn at random from the bag. Let

*E _{i}*(

*i*= 1, 2, 3) denote the event that its digit on the ticket is 2. Than:

There are 20 cards. 10 of these cards have the letter ‘I’ printed on them and the other 10 have the letter ‘T’ printed on them. If three cards are drawn without replacement and kept in the same order, the probability of making word IIT is: