MHB Find the probability that one receives a chocolate & a toffee

[mathlearn]

Out of 35 students a toffee is given to a randomly selected child & a chocolate is also given to a randomly selected child . FInd the probability that the same same child get both

(Party) Hmm my answer would be $\frac{1}{35}+\frac{1}{35}=\frac{2}{35}$

or I doubt whether is it $\frac{1}{35}*\frac{1}{35}$

 

[I like Serena]

Out of 35 students a toffee is given to a randomly selected child & a chocolate is also given to a randomly selected child . FInd the probability that the same same child get both

(Party) Hmm my answer would be $\frac{1}{35}+\frac{1}{35}=\frac{2}{35}$

or I doubt whether is it $\frac{1}{35}*\frac{1}{35}$

Hey mathlearn! ;)

Suppose the toffee is given to Anna, who is one of the 35 students, we don't care which one.
Now where does the chocolate land?
There are 2 possibilities: either it goes to Anna, or it goes to one of the other 34 students.
Care to consider what the chance is that Anna (who already has the toffee) gets the chocolate? (Wondering)

 

[mathlearn]

Hey mathlearn! ;)

Suppose the toffee is given to Anna, who is one of the 35 students, we don't care which one.
Now where does the chocolate land?
There are 2 possibilities: either it goes to Anna, or it goes to one of the other 34 students.
Care to consider what the chance is that Anna (who already has the toffee) gets the chocolate? (Wondering)

Probability that Anna gets the toffee $\frac{1}{35}$

Probability that Anna gets the chocolate $\frac{1}{35}$

Now depicting this information in a tree diagram.

View attachment 6080

Probability that she gets both $\frac{1}{35} * \frac{1}{35} = \frac{1}{1225} $

Correct?

Many Thanks (Smile)

 

[I like Serena]

Probability that Anna gets the toffee $\frac{1}{35}$

Probability that Anna gets the chocolate $\frac{1}{35}$

Now depicting this information in a tree diagram.
Probability that she gets both $\frac{1}{35} * \frac{1}{35} = \frac{1}{1225} $

Correct?

Many Thanks (Smile)

Not quite. (Shake)
It doesn't matter which student is Anna.
There is just the 1 chance in 35 that whoever got the toffee will get the chocolate.
So the chance that one student gets both the toffee and the chocolate is $\frac 1{35}$. (Thinking)

 

[HallsofIvy]

Out of 35 students a toffee is given to a randomly selected child & a chocolate is also given to a randomly selected child . FInd the probability that the same same child get both

(Party) Hmm my answer would be $\frac{1}{35}+\frac{1}{35}=\frac{2}{35}$

or I doubt whether is it $\frac{1}{35}*\frac{1}{35}$

Do you really think that the probability of being given a toffee and a chocolate could be greater than the probability of being given the toffee only?

 

[mathlearn]

Not quite. (Shake)
It doesn't matter which student is Anna.
There is just the 1 chance in 35 that whoever got the toffee will get the chocolate.
So the chance that one student gets both the toffee and the chocolate is $\frac 1{35}$. (Thinking)

This event ain't mutually exclusive , I guess (Thinking)

The probability that one gets a toffee and chocolate = $\frac 1{35}$

So got to agree but I wonder whether the rule of If or And of probability is used here

Do you really think that the probability of being given a toffee and a chocolate could be greater than the probability of being given the toffee only?

Thank you very much for the advice , Yes so now I see that the probability of getting the chocolate and the toffee is equal to the probability of getting the toffee :)

 

[MarkFL]

Suppose you number the 35 students, that is, assign each one a unique number from 1-35. If you are asked what is the probability that student #12 will get both candies, then you would find that probability is the square of 1/35. You have selected a student before the first candy is given out and so the 1/35 is applied twice.

In this problem though, a student isn't selected until the first candy is given, and only then are we to consider what is the probability that that student will then receive the second candy, which is just 1/35. :D

 

[mathlearn]

Suppose you number the 35 students, that is, assign each one a unique number from 1-35. If you are asked what is the probability that student #12 will get both candies, then you would find that probability is the square of 1/35. You have selected a student before the first candy is given out and so the 1/35 is applied twice.

In this problem though, a student isn't selected until the first candy is given, and only then are we to consider what is the probability that that student will then receive the second candy, which is just 1/35. :D

Thank you very much MarkFL (Happy) (Party)

So this case changes from the others as the child is not exactly told in the beginning but instead we choose he/she after the toffee is given

Many Thanks :D