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Question from Fatima, a parent:

My daughter has to complete the project in probability chapter. Her gave her a complete probability chapter and told her to do all the problems. Out of them some questions I am not getting
The question is like this please give me a detailed explanation.
When drawing cards without replacement from a standard 52-card deck, find the maximum number of cards you could possibly draw and still get
a. fewer than three black cards
b. fewer than six spades
c.few er than four face cards
d. fewer than two kings

Hi Fatima,

You said that your daughter's teacher told her to do all the problems in the chapter but then you said that you were having difficulty with some of them. I hope your daughter is working on the problems. I am going to show her how to sole part a. and then she should be able to do the rest.

If she is to draw as many cards as possible without drawing 3 black cards then she can start by drawing all 26 red cards. She can then draw 2 black cards but then she is stuck. All that is left are black cards and if she draws one she will have 3 black cards. Thus the maximum number of cards she can draw and still have fewer than 3 black cards is 26 + 2 = 28.

Now try the remaining parts,

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