The probability that Samantha will be accepted by the college of her choice and obtain a scholarship is 0.35. If the probability that she is accepted by the college is 0.65, find the probability that she will obtain a scholarship given that she is accepted by the college.
The probability is 0.35/0.65=7/13=0.54 (approximately)
Ah, probabilities and scholarships, quite the puzzling combination! To find the probability that Samantha will obtain a scholarship given that she is accepted by the college, we can use a little mathematical magic. Since we know the probability of Samantha being accepted by the college is 0.65, and the probability of her obtaining a scholarship is 0.35, we can set up a conditional probability equation. Let me do some calculations for you...
Take the probability of Samantha obtaining a scholarship (0.35) and divide it by the probability of her being accepted by the college (0.65). Drum roll, please...
0.35 / 0.65 = 0.5384615384615384 (approximately)
So, the probability that Samantha will obtain a scholarship given that she is accepted by the college is approximately 0.54. Let's hope that scholarship comes through and adds a little extra moolah to Samantha's college fund!
To find the probability that Samantha will obtain a scholarship given that she is accepted by the college, we can use the concept of conditional probability.
Conditional probability is the probability of an event occurring given that another event has already occurred.
Let's denote:
A = Samantha being accepted by the college
S = Samantha obtaining a scholarship
We are given:
P(A) = 0.65 (probability of Samantha being accepted by the college)
P(S|A) = 0.35 (probability of Samantha obtaining a scholarship given that she is accepted)
The probability that Samantha will obtain a scholarship given that she is accepted by the college can be calculated using the formula for conditional probability:
P(S|A) = P(S∩A) / P(A)
P(S∩A) represents the probability of both events, Samantha being accepted by the college and obtaining a scholarship, happening at the same time.
P(A) represents the probability of Samantha being accepted by the college.
We can rearrange the formula as follows:
P(S∩A) = P(S|A) * P(A)
Now we can substitute the given values into the formula:
P(S∩A) = 0.35 * 0.65
= 0.2275
The probability that Samantha will obtain a scholarship given that she is accepted by the college is 0.2275 or 22.75%.
To find the probability that Samantha will obtain a scholarship given that she is accepted by the college, you can use conditional probability. Conditional probability is a measure of the probability of an event happening, given that another event has already occurred.
Let's denote:
A = Samantha being accepted by the college
S = Samantha obtaining a scholarship
We are given:
P(A) = 0.65 (the probability that Samantha is accepted by the college)
P(S | A) = 0.35 (the probability that Samantha obtains a scholarship given that she is accepted by the college)
The conditional probability formula is:
P(S | A) = P(S and A) / P(A)
We can rearrange this formula to solve for P(S and A):
P(S and A) = P(S | A) * P(A)
Substituting the given values, we have:
P(S and A) = 0.35 * 0.65
P(S and A) = 0.2275
Therefore, the probability that Samantha will obtain a scholarship given that she is accepted by the college is 0.2275 or 22.75%.