In a bag, there are two types of candy bars: Snickers and Twix. Two items are chosen at random from the bag, without replacement. The probability of selecting a Snickers on the first draw is 71%. The probability of selecting a Snickers and then a Twix is 47%. What is the probability of selecting a Twix on the second draw, given that the first was a Snickers?
let the prob of picking a Twix be p, then
(.71)(p) = .47
p = .47/.71 = 47/71 = approx. .6619.. or about 66%
Well, it seems like the first draw prefers Snickers, but let's see what the numbers reveal.
To find the probability of selecting a Twix on the second draw, given that the first was a Snickers, we can use conditional probability. Conditional probability is like when you eat a bag of chips and then you conditionally want another bag of chips. It's all about those cravings!
Let's denote the probability of selecting a Twix on the second draw as P(Twix) and the probability of selecting a Snickers on the second draw given that the first was a Snickers as P(Twix|Snickers).
Now, we know that the probability of selecting a Snickers on the first draw is 71%, which we can write as P(Snickers) = 0.71.
We are also given that the probability of selecting a Snickers and then a Twix is 47%, which we can write as P(Snickers ∩ Twix) = 0.47.
Now, conditional probability states that P(A ∩ B) = P(A) * P(B|A). In this case, A represents selecting a Snickers on the first draw and B represents selecting a Twix on the second draw given that the first was a Snickers.
So, we can write P(Snickers ∩ Twix) = P(Snickers) * P(Twix|Snickers).
Plugging in the values we have, we get 0.47 = 0.71 * P(Twix|Snickers).
Now, let's solve for P(Twix|Snickers):
P(Twix|Snickers) = 0.47 / 0.71.
Calculating that, we find that P(Twix|Snickers) is approximately 0.662.
So, the probability of selecting a Twix on the second draw, given that the first was a Snickers, is about 66.2%! So, it looks like there's a decent chance to get your Twix fix after enjoying a Snickers. Enjoy your candies!
To find the probability of selecting a Twix on the second draw, given that the first draw was a Snickers, we can use conditional probability.
Let's denote:
- P(S) as the probability of selecting a Snickers on the first draw
- P(T) as the probability of selecting a Twix on the second draw
The probability of selecting a Snickers on the first draw is given as P(S) = 71% or 0.71.
The probability of selecting a Snickers and then a Twix is given as P(S ∩ T) = 47%.
Now, using conditional probability, we know that:
P(T|S) = (P(S ∩ T))/(P(S))
Plugging in the given values, we get:
P(T|S) = 0.47/0.71 = 0.66
Therefore, the probability of selecting a Twix on the second draw, given that the first draw was a Snickers, is 66% or 0.66.
To solve this problem, we can use conditional probability. The probability of selecting a Twix on the second draw, given that the first draw was a Snickers, can be calculated using the formula for conditional probability:
P(Twix on second draw | Snickers on first draw) = P(Twix on second draw and Snickers on first draw) / P(Snickers on first draw)
We are given that the probability of selecting a Snickers on the first draw is 71% (or 0.71 in decimal form). We also know that the probability of selecting a Snickers and then a Twix is 47% (or 0.47 in decimal form).
Let's denote the event of selecting a Twix on the second draw as T2 and the event of selecting a Snickers on the first draw as S1.
We are looking for P(T2 | S1). According to the formula for conditional probability, this is equal to P(T2 and S1) / P(S1).
P(S1) = probability of selecting a Snickers on the first draw (given as 0.71).
P(T2 and S1) = probability of selecting a Twix on the second draw and a Snickers on the first draw (given as 0.47).
Therefore,
P(Twix on second draw | Snickers on first draw) = P(T2 and S1) / P(S1)
= 0.47 / 0.71
Now we can calculate the probability:
P(Twix on second draw | Snickers on first draw) ≈ 0.66 or 66%
So, the probability of selecting a Twix on the second draw, given that the first draw was a Snickers, is approximately 0.66 or 66%.