Conditional probability- need to know how to identify the P(A and B) please

#1
Use the following information to determine your answers: A psychology experiment on memory was conducted which required participants to recall anywhere from 1 to 10 pieces of information. Based on many results, the (partial) probability distribution below was determined for the discrete random variable (X = number of pieces of information remembered (during a fixed time period)).
What is the missing probability P(X=7)? Your answer should include the second decimal place.
X = # information | probability:
1 | 0.0
2 | 0.02
3 | 0.04
4 | 0.07
5 | 0.15
6 | 0.18
7 | ?
8 | 0.14
9 | 0.11
10 | 0.05


I calculate the probability of 7 as 0.24 (1- sum of all other probabilities)

however I always get the below question wrong;

Given that the person recalls at least 7 pieces of information, what is the probability that they recall all 10 pieces? Please round to the second decimal place.

My logic is: P(A and B) = P(A) = P(10) = 0.05
and P(A|B) = 0.05/ P(B), 0.24 = 0.208 ~0.21

Can you help me understand what I am doing wrong, it is driving me crazy..

Thank you for your help :)
 

obh

Active Member
#2
Hi Moutazgendia,

P(A|B)= P(A ∩ B) / P(B)

A: X=10
B: X in (7,8,9,10) "least 7 pieces of information"

P(A|B) = P(X=10| p((x in (7,18,9,10)

Since A is included fully in B: P(A ∩ B)= P(A)

P(B)= P(X in (7,8,9,10))
 
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#3
Thank @obh for your reply. I am fairly new to statistics so excuse my naivety;

to make sure I understand you right.

P(A|B) would be = P(A and B)/ P(B) = P(X= commutative 7) / (P(X= commutative 10) = 0.7/ 1 ?

I think I am still not getting it.
 
#5
@obh so it should be like this:

P(A and B)= P(X=7)= 0.24

P(B)= P(X= 7+8+9+10) = 0.24+ 0.14+0.11+0.05 = 0.54

P(A|B) = 0.24/ 0.54 = 0.444

I tried that and still showed wrong answer
 
#7
@obh

Odd enough when I tried he below it gave me a right answer;

P(A and B) = P(X =10) = 0.05

P(B)= P(X = 0.24+0.14+0.11+0.05) = 0.54

0.5/0.54 = 0.09259 ~ 0.09

It doesn't make sense from the formula since I assumed the intersection is just the P(X =10), what am I missing
 

obh

Active Member
#9
A is the the event which you want to calculate
B the event you know that happen.
Now you need to calculate P(A|B)

Since A is included in B, A ∩ B = A
Is all clear now?
 

obh

Active Member
#13
long Long time since I used conditional probability...

The unconditional probability is P(X=10)=0.05
But your question is P(X=10 | (P(X in (7,8,9,10))