Aset of 5 cards are numbered from 1 to 5. two cards are drawn successively with replacement. let ee be the event "the second card has a (strictly) larger number than the first card." find p(e)p(e).

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes:

In this problem, we have that:

Total Outcomes

Format: (Card 1, Card 2)

(1,1), (1,2), (1,3), (1,4), (1,5)

(2,1), (2,2), (2,3), (2,4), (2,5)

(3,1), (3,2), (3,3), (3,4), (3,5)

(4,1), (4,2), (4,3), (4,4), (4,5)

(5,1), (5,2), (5,3), (5,4), (5,5)

There are 25 total outcomes

Let E be the event "the second card has a (strictly) larger number than the first card." Find P(E).

There are 10 outcomes in which the second card has a strictly larger number than the first card. They are:

(1,2), (1,3), (1,4), (1,5), (2,3), (2,4), (2,5), (3,4), (3,5), (4,5)

So

b.an increase in a causes b to decrease