Question

Q:2 Two-digit numbers, using the digit 5,6,7 are formed without repeating the digits
(1) E1 is the event that the number is divisible by 3.
(2). E2 is the event that the number is prime number​

Answer 1

Answer:

12th

Maths

Probability

Multiplication Theorem

Form two digit numbers usin...

MATHS

Form two digit numbers using the digit 0,1,2,3,4,5 without repeating the digits.

P is the event that the number so formed is even.

Q is the event that the number so formed is divisible by 3.

R is the event that the number so formed is greater than 50.

S is the sample space.

Which of the following options is correct?

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ANSWER

The given digits are 0,1,2,3,4,5

Number of two digit numbers that can be formed, as first place can be filed with 5 numbers and second place can be filed with another 5 numbers; 5×5=25

Now, number is an even number, with 0 at the end there can be 5 numbers, with 2 at the end there can be 4 numbers and with 4 at the end there can be 4 numbers. Hence, total numbers which are even =4+4+5=13

Numbers divisible by 3 are, 12,15,21,24,30,42,45,51,54

Thus, total numbers are, 9

There are only 4 number, viz. 51,52,53,54 which are greater than 50

Hence, n(S)=25,n(P)=13,n(Q)=9,n(R)=4