Suppose 5 cards are dealt from an ordinary deck of 52 playing cards. (a) What is the probability that exactly 2 of the cards will be face cards? (b) What is the probability that at least 1 of the cards will be a queen? (a) The probability that exactly 2 of the cards will be face cards is .2509. (Round to four decimal places as needed.) (b) The probability that at least 1 of the cards will be a queen is (Round to four decimal places as needed.)
Suppose 5 cards are dealt from an ordinary deck of 52 playing cards. (a) What is the probability that exactly 2 of the cards will be face cards? (b) What is the probability that at least 1 of the cards will be a queen? (a) The probability that exactly 2 of the cards will be face cards is .2509. (Round to four decimal places as needed.) (b) The probability that at least 1 of the cards will be a queen is (Round to four decimal places as needed.)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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![**Problem Statement**:
Suppose 5 cards are dealt from an ordinary deck of 52 playing cards.
- **(a)** What is the probability that exactly 2 of the cards will be face cards?
- **(b)** What is the probability that at least 1 of the cards will be a queen?
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**Solution**:
- **(a)** The probability that exactly 2 of the cards will be face cards is **0.2509**. (Round to four decimal places as needed.)
- **(b)** The probability that at least 1 of the cards will be a queen is **[Blank for user input]**. (Round to four decimal places as needed.)
**Explanation**:
- **Face Cards**: In a standard deck of 52 cards, there are 12 face cards (Jack, Queen, King of each suit: Clubs, Diamonds, Hearts, Spades).
- **Queens**: There are 4 queens in the deck (one of each suit).
This exercise requires understanding of probability with combinations, where the user must calculate using the formula for combinations to determine the chances of specific outcomes in card draws.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbe7e575d-dfd7-411c-ad5f-62e2be64ba9f%2F2790df52-b17d-48ca-afae-88272b23b254%2Fflmw52d_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement**:
Suppose 5 cards are dealt from an ordinary deck of 52 playing cards.
- **(a)** What is the probability that exactly 2 of the cards will be face cards?
- **(b)** What is the probability that at least 1 of the cards will be a queen?
---
**Solution**:
- **(a)** The probability that exactly 2 of the cards will be face cards is **0.2509**. (Round to four decimal places as needed.)
- **(b)** The probability that at least 1 of the cards will be a queen is **[Blank for user input]**. (Round to four decimal places as needed.)
**Explanation**:
- **Face Cards**: In a standard deck of 52 cards, there are 12 face cards (Jack, Queen, King of each suit: Clubs, Diamonds, Hearts, Spades).
- **Queens**: There are 4 queens in the deck (one of each suit).
This exercise requires understanding of probability with combinations, where the user must calculate using the formula for combinations to determine the chances of specific outcomes in card draws.
![**Acceptance Scheme and Probability Calculation**
A manufacturing company uses an acceptance scheme on items from a production line before they are shipped. The plan is a two-stage one. Boxes of 24 items are readied for shipment, and a sample of 5 items is tested for defectives. If any defectives are found, the entire box is sent back for 100% screening. If no defectives are found, the box is shipped.
**Questions:**
(a) What is the probability that a box containing 3 defectives will be shipped?
(b) What is the probability that a box containing only 1 defective will be sent back for screening?
---
**Calculation:**
(a) The probability that a box containing 3 defectives will be shipped is [____].
*(Round to four decimal places as needed.)*](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbe7e575d-dfd7-411c-ad5f-62e2be64ba9f%2F2790df52-b17d-48ca-afae-88272b23b254%2Fj3sx31n_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Acceptance Scheme and Probability Calculation**
A manufacturing company uses an acceptance scheme on items from a production line before they are shipped. The plan is a two-stage one. Boxes of 24 items are readied for shipment, and a sample of 5 items is tested for defectives. If any defectives are found, the entire box is sent back for 100% screening. If no defectives are found, the box is shipped.
**Questions:**
(a) What is the probability that a box containing 3 defectives will be shipped?
(b) What is the probability that a box containing only 1 defective will be sent back for screening?
---
**Calculation:**
(a) The probability that a box containing 3 defectives will be shipped is [____].
*(Round to four decimal places as needed.)*
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