Question

An ordinary deck of 52 cards is well-shuffled, and then the cards are turned

face up one by one until a face card (K,Q,J) appears. Find the expected

number of cards that are face up. Show and explain plz

Answer 1

Answer:-

Given That:-

An ordinary deck of 52 cards is well-shuffled, and then the cards are turned

face up one by one until a face card (K,Q,J) appears.

we are given that the cards of an ordinary deck of 52 cards are turned face up one by one until an ace appears .we need to find the expected number of the cards that are face up.

Let X be the number of the cards to be turned face up until an ace appears. Then

we need to find

The expected value of a random variable X with the set of the possible values A and the probability mass function P(X) is defined as

Now ,we need to find ​​​​​​

Let A be the events that no ace appears among the first cards that are turned face up and B be the event that cards turned face up is an ace.

Thus, we have

On using the law of multiplication ,we get

Thus, we get

On using the summation calculation ,we get