Find the conditional probability. Suppose one card is selected at random from an ordinary deck of 52 playing cards.
Let A = event a queen is selected
B = event a diamond is selected
Determine P(B[A)
How do you go about solving this one?
I know there are 4 queens, 13 diamonds
13/52 4/52 = 17/52
Is that correct?
One last question...
The age distribution of students at a community college is given below.
Age(years) # Numbers of students
Under 21 - 411 students
21- 25 - 407 students
26-30 - 201 students
31-35 - 51 students
Over 35 - 26 students
A student from the community college is selected at random. Find the conditional probability that the student is between 26- 30 given that he or she is at least 26.
I would also like to know how to work this problem out.
Please help.
If a queen is selected, there are 51 cards left, and 4 diamonds. So Pr(B given A) is 4/51.
If she is at least 26, then there are a total of 201+51+ 26 students in that age pool. Pr of being in 26-30 age group then is 201/total above
Probabality is always the number of likely draws out of the total possible pool.
To solve the first problem, you correctly calculated the probability of selecting a queen (A) and a diamond (B) from the deck of cards. There are 4 queens and 13 diamonds out of 52 cards. So, the probability of selecting a queen and a diamond is (4/52) * (13/52) = 1/52.
However, you are trying to find the conditional probability of selecting a diamond given that a queen has been selected. In this case, you need to consider that there are 51 cards left after selecting a queen, and out of those 51 cards, only 4 are diamonds. So, the conditional probability P(B|A) is (4/51).
For the second problem, you want to find the conditional probability that a student is between 26-30 years old given that they are at least 26 years old. To do this, you need to consider the number of students in the age group 26-30 and the total number of students who are at least 26.
From the given data, there are 201 students in the age group 26-30, and the total number of students who are at least 26 is (201+51+26). Therefore, the conditional probability P(26-30|at least 26) is (201/(201+51+26)).
Remember, conditional probability is the probability of an event occurring given that another event has already occurred. In these problems, you calculate the conditional probability by considering the number of favorable outcomes (cards or students) in the specified condition, divided by the total number of outcomes in the given condition.