Consider aexperimant of PickingThree Cards at random lors tteaisequcefroma Standard deck of 52 Cards,let A: be the event that the i th Cardis red ( for 1 s i <3) whot is the Probability that allthree cards are red?2) what ia Prob CAg)? Prob(A,) ? Prob(Aa)?3) Are A, and A, in dep endent ( Explain

Answered: Consider a experimant of Picking Three…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

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Question

Consider a
experimant of Picking
Three Cards at random lors tteaisequce
from
a Standard deck of 52 Cards,
let A: be the event that the i th Card
is red ( for 1 s i <3
) whot is the Probability that all
three cards are red?
2) what ia Prob CAg)? Prob(A,) ? Prob(Aa)?
3) Are A, and A, in dep endent ( Explain

Expert Solution

Step 1

Note: Hello! Thanks for the question. There is no information about the type of selection (with replacement or without replacement). Hence, we are providing the solution for both the cases

From the given information,

Three cards are selected at random from a deck of 52 cards.

Let A_i be the event that the ith card is red for $1 \leq i \leq 3$ .

In the deck of 52 cards, there are 26 red cards and 26 black cards.

Case 1: With replacement:

The probability that all three cards are red is,

$P (a l l t h r e e r e d) = \frac{26}{52} * \frac{26}{52} * \frac{26}{52} = \frac{1}{2} * \frac{1}{2} * \frac{1}{2} = 0.125$

Step 2

$P (A_{1}) = \frac{26}{52} = \frac{1}{2} = 0.5$

$P (A_{2}) = \frac{26}{52} = \frac{1}{2} = 0.5$

$P (A_{3}) = \frac{26}{52} = \frac{1}{2} = 0.5$

Here, the happing of selecting first red ball does not affect the happening of selecting second red ball because the selections are done by with replacement.

Hence, the selections are independent.

That is, the events A1 and A2 are independent.

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