{"id":524,"date":"2022-04-13T09:37:24","date_gmt":"2022-04-13T09:37:24","guid":{"rendered":"http:\/\/9thclass.deltapublications.in\/?page_id=524"},"modified":"2024-07-12T11:57:36","modified_gmt":"2024-07-12T11:57:36","slug":"ee-5-probability-of-independent-and-dependent-events","status":"publish","type":"page","link":"https:\/\/9thclass.deltapublications.in\/index.php\/ee-5-probability-of-independent-and-dependent-events\/","title":{"rendered":"EE.5 Probability of independent and dependent events"},"content":{"rendered":"\n

Probability of independent and dependent events<\/strong><\/h2>\n\n\n\n

key notes :<\/p>\n\n\n\n

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Two events are independent if the outcome of the first event does not affect the outcome of the second event.<\/p>\n\n\n\n

The only factors of a prime number are 1 and itself. The number 1 is neither prime nor composite.<\/p>\n<\/div><\/div>\n\n\n\n

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The probability is the number of favorable outcomes out of the number of possible outcomes.<\/p>\n<\/div><\/div>\n\n\n\n

Learn with an example<\/strong><\/p>\n\n\n\n

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\u27a1\ufe0f You roll a 6-sided die two times.<\/p>\n\n\n

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\"\"<\/figure><\/div>\n\n\n

What is the probability of rolling a number less than 4 and then rolling a prime number?<\/strong><\/p>\n\n\n\n

Write your answer as a percentage.<\/em><\/p>\n\n\n\n

______ %<\/p>\n<\/div><\/div>\n\n\n\n

The events less than 4<\/strong> and prime<\/strong> are independent. The first roll does not affect the second roll.<\/p>\n\n\n\n

Find P(less than 4). The die has 6 sides, numbered 1, 2, 3, 4, 5 and 6. The numbers less than 4 are 1, 2 and 3. There are 3 numbers less than 4.<\/p>\n\n\n\n

P(less than 4) = 3\/6<\/p>\n\n\n\n

Find P(prime). The prime numbers are 2, 3 and 5.<\/p>\n\n\n\n

P(less than 4) x P(prime) = 3\/6 x 3\/6<\/p>\n\n\n\n

= 9\/36<\/p>\n\n\n\n

Write your answer as a decimal. Then convert your answer to a percentage.<\/p>\n\n\n\n

9\/36 = 0.25 = 25%<\/p>\n\n\n\n

The probability of rolling a number less than 4 and then rolling a prime number is 25%.<\/p>\n<\/div><\/div>\n\n\n\n

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\u27a1\ufe0f You pick a card at random. Without putting the first card back, you pick a second card at random.<\/p>\n\n\n

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\"\"<\/figure><\/div>\n\n\n

What is the probability of picking an even number and then picking an even number?<\/strong><\/p>\n\n\n\n

Simplify your answer and write it as a fraction or whole number.<\/em><\/p>\n<\/div><\/div>\n\n\n\n

Find P(even). There are 4 cards, numbered 1, 2, 3 and 4. The even numbers are 2 and 4. There are 2 even numbers.<\/p>\n\n\n\n

P(even) = 2\/4<\/p>\n\n\n\n

Now find the probability of picking an even number once you have already picked an even number.<\/p>\n\n\n\n

There are 3 cards remaining. One of those cards is an even number.<\/p>\n\n\n\n

After you have picked an even number, the probability of picking an even number is 1\/3 , <\/p>\n\n\n\n

Find the probability of picking an even number and then picking an even number. Multiply P(even) by P(even).<\/p>\n\n\n\n

P(even) x P(even) = 2\/4 x 1\/3<\/p>\n\n\n\n

= 2\/12<\/p>\n\n\n\n

Write your answer in simplest form.<\/p>\n\n\n\n

2\/12 = 1\/6<\/p>\n\n\n\n

The probability of picking an even number and then picking an even number is 1\/6 .<\/p>\n<\/div><\/div>\n\n\n\n

\n
\n

\u27a1\ufe0f You roll a 6-sided die two times.<\/p>\n\n\n

\n
\"\"<\/figure><\/div>\n\n\n

What is the probability of rolling a factor of 12 and then rolling a number less than 4?<\/strong><\/p>\n\n\n\n

Simplify your answer and write it as a fraction or whole number.<\/em><\/p>\n<\/div><\/div>\n\n\n\n

The events factor of 12<\/strong> and less than 4<\/strong> are independent. The first roll does not affect the second roll.<\/p>\n\n\n\n

Find P(factor of 12). The die has 6 sides, numbered 1, 2, 3, 4, 5 and 6. The factors of 12 are 1, 2, 3, 4 and 6.<\/p>\n\n\n\n

P(factor of 12) = 5\/6<\/p>\n\n\n\n

Find P(less than 4). The numbers less than 4 are 1, 2 and 3. There are 3 numbers less than 4.<\/p>\n\n\n\n

P(less than 4) = 3\/6<\/p>\n\n\n\n

Find the probability of rolling a factor of 12 and then rolling a number less than 4. Multiply P(factor of 12) by P(less than 4).<\/p>\n\n\n\n

P(factor of 12) x P(less than 4) = 5\/6 x 3\/6<\/p>\n\n\n\n

= 15\/36<\/p>\n\n\n\n

Write your answer in simplest form.<\/p>\n\n\n\n

15\/36 = 5\/12<\/p>\n\n\n\n

The probability of rolling a factor of 12 and then rolling a number less than 4 is 5\/12 .<\/p>\n<\/div><\/div>\n\n\n\n

let’s practice!<\/p>\n\n\n\n

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\"\"<\/a><\/figure>\n<\/div>\n\n\n\n
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\"\"<\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

Probability of independent and dependent events key notes : Two events are independent if the outcome of the first event does not affect the outcome of the second event. The only factors of a prime number are 1 and itself. The number 1 is neither prime nor composite. The probability is the number of favorableContinue reading “EE.5 Probability of independent and dependent events”<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"om_disable_all_campaigns":false,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"class_list":["post-524","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/524","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/comments?post=524"}],"version-history":[{"count":13,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/524\/revisions"}],"predecessor-version":[{"id":14141,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/524\/revisions\/14141"}],"wp:attachment":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=524"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}