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Selecting Cards The red face cards and the black cards numbered 2–9 are put into a bag. Four cards are drawn at random without replacement. Find the following probabilities.$$\begin{array}{l}{\text { a. All } 4 \text { cards are red. }} \\ {\text { b. } 2 \text { cards are red and } 2 \text { cards are black. }} \\ {\text { c. At least } 1 \text { of the cards is red. }} \\ {\text { d. All } 4 \text { cards are black. }}\end{array}$$

Intro Stats / AP Statistics

Chapter 4

Probability and Counting Rules

Section 5

Sampling and Data

Probability Topics

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Lectures

0:00

01:11

Suppose that 4 cards are d…

00:41

If two cards are drawn wit…

04:17

Drawing a Card Four cards …

01:04

01:17

Find the probability for t…

01:31

In Exercises 21 - 24, f…

01:21

Four cards are drawn from …

00:40

03:12

In a deck of cards there a…

03:28

Drawing a Card A card is d…

Okay, so in this question, this based on selecting cards, there are red cards. Are there black card soldier? It's a number from 2 to 9. So 2 to 9 means we know in a suit there will be eight cars, silver either. So total in total harmony cards will be there will be 16 black cards. The bigger Onda 16 credit cards still didn't 16 black and 16 red cards. Okay, Now is the first question it is asking. What is the probability that all four cards are red? All four Car star, right? So basically it is out off. 32 cars were selecting for red cards, so total number of selection will be 32 C four. Now, how many black cards are there? You can see 16 black cards are so out of 16 black cards will be selected for black cards. This will be the required probably couldn't in this second part of the question, it is asking probability off two black cards on tour articles. So again, we're selecting four cards from 32 so it will be basically 32 C four on your selecting two black cards out of 16 can take 16 32 on selecting to read from 16 red that you can do by 16 ft. This will be required, probably no. In the third part of the question, it is asking At least one card is right. Probably off. At least one is red. So whenever this kind of questions are coming, we can do by using one minus, probably off. None is thread. That means no card were selected is a red card. That means you can't be written us when minus probability off. All cars are black, right? So how we right answer is one minus, probably of old cars are blackness. We can write one minus from 16 black cards, 16 red cards. We're not selecting anything remaining. 16 black cuts. We're selecting four cuts on total number of selection will be what it is always 32 C four. So this will be the required probability. Andi In the last part of the question, it is asking us to find the probability that all four cards are black. All four cards are black. So how we find this card? This question is exactly similar to the first question. All forum black means out of 16 black guards you are to select for in total number of selection will be out of 32 years selecting for this other required probabilities. Now we can simplify this question, right? We can simplify and find the answer. For example, 16 c two by 32 c. Four. We'll see. What is the simplified Ansari's So 16 c two 16 34 by 32 c. Forrester We'll be getting answer zero point 050 six. This will be that required probability. Now, in the second part of the question, we're getting answers. 16 seed to even to 16 ft so that also we can simplify. So simplified answer for that. Okay, we'll find out how much it will come 16. 32 in Goa. 16 C two by 32 C four. Right. So when we simplify that, we'll be getting answer point for zero point for the role. Come. Okay, now similarly, this question Third question. Also, we find the simplified answer. We get one minus, we get 0.94 nine. Foresti required. Answer Now, this last case again, the values save. You can see that first question and second last question border, same values of them. So here also will be getting the same value 0.506 This happy require the probability in simplified form.

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