The probability that the number 11 was picked given that the sum of the number was even is 0.4. Option d is the right choice.
The probability of event A occurring given that event B has already occurred is called the conditional probability of event A given event B. It is denoted by P(A|B) and can be calculated using the following formula:
P(A|B) = P(A ∩ B) / P(B)
where:
P(A ∩ B) is the probability of both event A and event B occurring.
P(B) is the probability of event B occurring.
In this case, event A is the event that the number 11 was picked. Event B is the event that the sum of the two numbers is even.
To calculate P(A|B), we first need to calculate P(A ∩ B) and P(B).
P(A ∩ B) is the number of ways to pick a pair of numbers that includes 11 and has an even sum. There are 4 such pairs: (11, 2), (11, 4), (11, 12), and (11, 14).
P(B) is the number of ways to pick a pair of numbers that has an even sum. There are 10 such pairs.
Therefore, P(A|B) = 4/10 = 0.4.
So the answer is option d. 0.4
Question:-
A pair of numbers is picked up randomly (without replacement ) from the set
{1, 2, 3, 5, 7, 11, 12, 13, 17, 19}. The probability that the number 11 was picked given that the sum of the number was even is nearly:
a. 0.1
b. 0.25
c. 0.24
d. 0.4