/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 446 Find the probability that a face... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 8: Problem 446

Find the probability that a face card is drawn on the first draw and an ace on the second in two consecutive draws, without replacement, from a standard deck of cards.

Short Answer

Expert verified
The probability of drawing a face card on the first draw and an ace on the second draw in two consecutive draws, without replacement, from a standard deck of cards is approximately \(\frac{1}{55.25}\).

Step by step solution

01

Probability of Drawing a Face Card on the First Draw

In a standard deck of 52 cards, there are 12 face cards (4 each of Kings, Queens, and Jacks). The probability of drawing a face card in the first draw can be calculated by dividing the number of face cards by the total number of cards in the deck: First draw probability (face card) = \(\frac{Number \ of\ face\ cards}{Total\ number\ of\ cards}\) First draw probability (face card) = \(\frac{12}{52}\)
02

Probability of Drawing an Ace on the Second Draw

Since there is no replacement, after drawing a face card there will be 51 cards left in the deck. Since there are 4 aces in the deck, the probability of drawing an ace for the second draw is: Second draw probability (ace) = \(\frac{Number \ of\ aces}{Remaining\ number\ of\ cards}\) Second draw probability (ace) = \(\frac{4}{51}\)
03

Calculate the Probability of Both Events Occurring Consecutively

Now that we have calculated the probabilities of each draw separately, we need to find the probability of both events occurring consecutively. To do this, we simply multiply the individual probabilities together: Probability (face card & ace) = First draw probability (face card) 脳 Second draw probability (ace) Probability (face card & ace) = \(\frac{12}{52} 脳 \frac{4}{51}\)
04

Simplify the Result

Now we can simplify the fraction: Probability (face card & ace) = \(\frac{12 脳 4}{52 脳 51}\) Probability (face card & ace) = \(\frac{48}{2652}\) Probability (face card & ace) 鈮� \(\frac{1}{55.25}\) The probability of drawing a face card on the first draw and an ace on the second draw in two consecutive draws, without replacement, from a standard deck of cards is approximately \(\frac{1}{55.25}\).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

From an ordinary deck of playing cards, cards are drawn successively at random and without replacement. Compute the probability that the third spade appears on the sixth draw.

A traffic count at a highway junction revealed that out of 5,000 cars that passed through the junction in 1 week, 3,000 turned to the right. Find the probability that a car will turn (a) to the right, and to the left.

If a pair of dice is tossed twice, find the probability of obtaining 5 on both tosses.

Find the probability that three successive face cards are drawn in three successive draws (without replacement) from a deck of cards. Define Events \(\mathrm{A}, \mathrm{B}\), and \(\mathrm{C}\) as follows: Event A: a face card is drawn on the first draw, Event \(B\) : a face card is drawn on the second draw, Event \(C\) : a face card is drawn on the third draw.

A box contains 4 black marbles, 3 red marbles, and 2 white marbles. What is the probability that a black marble, then a red marble, then a white marble is drawn without replacement?
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Applied Mathematics

Read Explanation

Discrete Mathematics

Read Explanation

Mechanics Maths

Read Explanation

Calculus

Read Explanation

Decision Maths

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.