Question

A locker combination consists of two nonzero digits, and each combination consists of different digits. Event A is defined as choosing an odd number as the first digit, and event B is defined as choosing an odd number as the second digit.
If a combination is picked at random, with each possible locker combination being equally likely, what is P(A and B) expressed in simplest form?

A. 5/18
B. 4/9
C. 1/2
D. 5/9

Answer 1

The correct answer is option B which is P ( A|B) will be ( 4 / 9 ).

What is probability?

Probability is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

Given that:-

• A locker combination consists of two nonzero digits, and each combination consists of different digits. Event A is defined as choosing an odd number as the first digit, and event B is defined as choosing an odd number as the second digit.

The total sample will have 9 numbers

S = { 1,2,3,4,5,6,7,8,9} = 9

Even Number = { 2,4,6,8} = 4

Odd Number  = { 1,3,5,7,9} = 5

P ( A ) = ( 4 / 9 )

P ( B ) = ( 5 / 9 )

The probability will be calculated as:-

P( A:B ) = $\dfrac{P(A)\times P(B)}{P(B)}$

P( A:B ) =$\dfrac{( 5/9 ) ( 4/9 )}{5 / 9 }$

P( A:B ) = 4 / 9

Therefore the correct answer is option B which is P ( A|B) will be ( 4 / 9 ).

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