{"id":187741,"date":"2025-02-06T06:03:05","date_gmt":"2025-02-06T06:03:05","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=187741"},"modified":"2025-02-06T06:03:07","modified_gmt":"2025-02-06T06:03:07","slug":"determine-the-required-value-of-the-missing-probability-to-make-the-distribution-a-discrete-probability-distribution","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/02\/06\/determine-the-required-value-of-the-missing-probability-to-make-the-distribution-a-discrete-probability-distribution\/","title":{"rendered":"Determine The Required Value Of The Missing Probability To Make The Distribution A Discrete Probability Distribution"},"content":{"rendered":"\n<p>Determine The Required Value Of The Missing Probability To Make The Distribution A Discrete Probability Distribution<\/p>\n\n\n\n<p>A X 3 4 5 6 P(X) 0.34 ? 0.23 0.18 <\/p>\n\n\n\n<p>P(4)-(Type An Integer Or A Decimal) Ty<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/02\/image-47.png\" alt=\"\" class=\"wp-image-187742\"\/><\/figure>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\"><strong>The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n<p>To determine the missing probability ( P(4) ), we need to ensure that the given probability distribution satisfies the condition of a discrete probability distribution.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Step 1: Understanding a Discrete Probability Distribution<\/strong><\/h3>\n\n\n\n<p>A discrete probability distribution must satisfy two key conditions:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Each probability must be between 0 and 1<\/strong>: That is, ( 0 \\leq P(X) \\leq 1 ) for all values of ( X ).<\/li>\n\n\n\n<li><strong>The sum of all probabilities must equal 1<\/strong>: That is,<br>[<br>P(3) + P(4) + P(5) + P(6) = 1<br>]<\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Step 2: Setting Up the Equation<\/strong><\/h3>\n\n\n\n<p>From the given data:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>( P(3) = 0.34 )<\/li>\n\n\n\n<li>( P(4) = ? )<\/li>\n\n\n\n<li>( P(5) = 0.23 )<\/li>\n\n\n\n<li>( P(6) = 0.18 )<\/li>\n<\/ul>\n\n\n\n<p>Using the probability sum rule:<br>[<br>0.34 + P(4) + 0.23 + 0.18 = 1<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Step 3: Solving for ( P(4) )<\/strong><\/h3>\n\n\n\n<p>First, sum up the known probabilities:<br>[<br>0.34 + 0.23 + 0.18 = 0.75<br>]<\/p>\n\n\n\n<p>Now, solve for ( P(4) ):<br>[<br>P(4) = 1 &#8211; 0.75<br>]<\/p>\n\n\n\n<p>[<br>P(4) = 0.25<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Final Answer: ( P(4) = 0.25 )<\/strong><\/h3>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Explanation (300 Words)<\/strong><\/h3>\n\n\n\n<p>A probability distribution represents how probabilities are assigned to discrete outcomes of a random variable. In this case, the random variable ( X ) can take values 3, 4, 5, or 6, and each value has a corresponding probability ( P(X) ).<\/p>\n\n\n\n<p>To ensure that this is a valid probability distribution, the sum of all probabilities must equal 1. Given that ( P(3) = 0.34 ), ( P(5) = 0.23 ), and ( P(6) = 0.18 ), we calculated the sum of these known probabilities as:<\/p>\n\n\n\n<p>[<br>0.34 + 0.23 + 0.18 = 0.75<br>]<\/p>\n\n\n\n<p>Since the total probability must be 1, the missing probability ( P(4) ) is found by subtracting this sum from 1:<\/p>\n\n\n\n<p>[<br>P(4) = 1 &#8211; 0.75 = 0.25<br>]<\/p>\n\n\n\n<p>Thus, ( P(4) = 0.25 ), making the probability distribution complete and valid.<\/p>\n\n\n\n<p>This process ensures that the given data meets the conditions of a discrete probability distribution: all probabilities are within the range [0,1], and their total sum is exactly 1.<\/p>\n\n\n\n<p>Let me know if you need further clarification! \ud83d\ude0a<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Determine The Required Value Of The Missing Probability To Make The Distribution A Discrete Probability Distribution A X 3 4 5 6 P(X) 0.34 ? 0.23 0.18 P(4)-(Type An Integer Or A Decimal) Ty The Correct Answer and Explanation is : To determine the missing probability ( P(4) ), we need to ensure that the 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