Answer:
The two statements provided are correct.
- P(A|B) = P(A), the conditional probability that Ebru selects a 2 given that she has chosen a
spade is equal to the probability that Ebru selects a 2.
- P(B|A) = P(B), the conditional probability that Ebru selects a spade given that she has
chosen a 2 is equal to the probability that Ebru selects a spade.
Step-by-step explanation:
In total, there are 52 cards.
There are 4 suites; hearts, clubs, diamonds, and spades.
Meaning there are
13 hearts, 13 clubs, 13 diamonds and 13 spades.
Each suit contains cards numbered 2 – 10, a jack, a queen, a king, and an ace.
Let A be the event that the card is a 2 and B be the event that it is a spade.
P(A) = n(cards that are 2s) ÷ n (total)
P(A) = (4/52) = (1/13)
P(B) = n(spades) ÷ n(total)
P(B) = (13/52) = (1/4)
The conditional probability, P(A|B) is given as
P(A|B) = P(A n B) ÷ P(B)
For this cards question,
P(A n B) = n(a spade that is a 2) ÷ n(total)
P(A n B) = (1/52)
So, to investigate,
P(A|B) = P(A), the conditional probability that Ebru selects a 2 given that she has chosen a
spade is equal to the probability that Ebru selects a 2.
P(A|B) = P(A n B) ÷ P(B) = (1/52) ÷ (1/4) = (1/13) = P(A)
Hence, this statement is true!
P(B|A) = P(B), the conditional probability that Ebru selects a spade given that she has
chosen a 2 is equal to the probability that Ebru selects a spade.
P(B|A) = P(B n A) ÷ P(A) = (1/52) ÷ (1/13) = (1/4) = P(B)
This statement is also true!
Hope this Helps!!!
