Probability - 8

Q. 3- Three whole no. is selected at random and multipliea find the chance that-

(1) Their product is divisible by 5 but not 10.

(2)Divisible by 10 .

(3) is an even no.

Ans- E₁ Digits at unit plce of 3 whole no. 1, 3, 7, 9

E₂ digits at unit place of whole no. is 1, 3, 5, 7, 9

E₃ digits at unit place of 3 whole no;s is 1, 2, 3, 4, 5, 6, 7, 8, 9 there are 10 digits -

P(E₁) = I^st Whole no. , 2^nd Whole no., 3^rd Whole no., =

P(E₂) = =

P(E₃) = =

divisible by 5 not by 10 at unit place only 5 is there .

(1) P(divisible by 5 not by 10 ) = P(E₂) - P(E₁)

= - =

=

(2) (divisible by 10 means last digit is zers )

= 1 - - =

Dumb question -

Q. How P(disivible by 5 not by 10 ) = P(E₂) - P(E₁)

Ans- Divisible by 5 not 10 only when at uniy place only 5 is there.

P(E₁) = Prob. of having 1, 3, 7, 9 at unit place

P(E₂) = Prob. of having '5' at unit place

= P(E₂) - P(E₁)

=P (divisible by 5 not by 10)

(3) P(even) = 1 - P(E₂) [ have digit 2, 4, 6, 8 at unit place ]
= 1 -
=

Key words

• Sample space
• Equally likely events
• Mutually exclusive events
• Exhaustive events
• Independent events
• Expectation value
• Bernoulli's trial
• Boye's theorem (Total frobability theorem)
• Infinite sample space.