Question

In: Statistics and Probability

Suppose you have a deck of 40 cards, containing 10 red cards and 30 black cards....

Suppose you have a deck of 40 cards, containing 10 red cards and 30 black cards. A player draws 7 cards from the deck and places them into their hand. The remaining deck of 33 cards has 5 red cards and 5 black cards in the top 10 cards. The other 23 cards in the remaining deck are unknown color. What is the probability of the player's hand having 0,1,2,3,4,5 red cards?

Solutions

Expert Solution

Total number of cards = 40

Total Number of red cards = 10

Total Number of black cards = 30

A player draws 7 cards from the deck and places them into their hand.

The remaining deck of 33 cards has 5 red cards and 5 black cards in the top 10 cards.

So,

Number of red cards remaining = 10 - 5 = 5

Number of black card remaining = 30 - 5 = 25

Total number of cards = 5 + 25 = 30

We have to draw 7 cards from 30 cards

Now

the probability of the player's hand having 0 red cards

= probability of the player's hand having all the 7 cards black

ii)

The probability of the player's hand having 1 red cards

iii)

The probability of the player's hand having 2 red cards

iv)

The probability of the player's hand having 3 red cards

The probability of the player's hand having 4 red cards

vi)

The probability of the player's hand having 5 red cards

orchestra answered 1 year ago

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