{"id":187739,"date":"2025-02-06T05:42:01","date_gmt":"2025-02-06T05:42:01","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=187739"},"modified":"2025-02-06T05:42:03","modified_gmt":"2025-02-06T05:42:03","slug":"find-the-missing-probability-in-the-table-below","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/02\/06\/find-the-missing-probability-in-the-table-below\/","title":{"rendered":"find the missing probability in the table below"},"content":{"rendered":"\n

find the missing probability in the table below, assume that X can only be 0<\/p>\n\n\n\n

X P(X)<\/p>\n\n\n\n

0 0.01<\/p>\n\n\n\n

1 0.15<\/p>\n\n\n\n

2 0.25<\/p>\n\n\n\n

3 0.10<\/p>\n\n\n\n

4 0.20<\/p>\n\n\n\n

5 ???<\/p>\n\n\n\n

a.)Given the rest of the table, what is P(X =5)?<\/p>\n\n\n\n

b) What is P(X=2)?<\/p>\n\n\n\n

c) What is P(X 3)?<\/p>\n\n\n\n

d) What is E(X)?<\/p>\n\n\n\n

The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n

Let’s solve the missing probability and answer the related probability questions.<\/p>\n\n\n\n

Given Probability Table:<\/h3>\n\n\n\n
X<\/th>P(X)<\/th><\/tr><\/thead>
0<\/td>0.01<\/td><\/tr>
1<\/td>0.15<\/td><\/tr>
2<\/td>0.25<\/td><\/tr>
3<\/td>0.10<\/td><\/tr>
4<\/td>0.20<\/td><\/tr>
5<\/td>???<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

(a) Find ( P(X = 5) ):<\/h3>\n\n\n\n

Since the sum of all probabilities in a probability distribution must equal 1:<\/p>\n\n\n\n

[
P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4) + P(X=5) = 1
]<\/p>\n\n\n\n

Substituting the known values:<\/p>\n\n\n\n

[
0.01 + 0.15 + 0.25 + 0.10 + 0.20 + P(X=5) = 1
]<\/p>\n\n\n\n

[
0.71 + P(X=5) = 1
]<\/p>\n\n\n\n

[
P(X=5) = 1 – 0.71 = 0.29
]<\/p>\n\n\n\n

(b) Find ( P(X=2) ):<\/h3>\n\n\n\n

From the table:<\/p>\n\n\n\n

[
P(X=2) = 0.25
]<\/p>\n\n\n\n

(c) Find ( P(X \\geq 3) ):<\/h3>\n\n\n\n

[
P(X \\geq 3) = P(X=3) + P(X=4) + P(X=5)
]<\/p>\n\n\n\n

[
P(X \\geq 3) = 0.10 + 0.20 + 0.29
]<\/p>\n\n\n\n

[
P(X \\geq 3) = 0.59
]<\/p>\n\n\n\n

(d) Compute the Expected Value ( E(X) ):<\/h3>\n\n\n\n

The expected value ( E(X) ) is calculated as:<\/p>\n\n\n\n

[
E(X) = \\sum X \\cdot P(X)
]<\/p>\n\n\n\n

[
E(X) = (0 \\times 0.01) + (1 \\times 0.15) + (2 \\times 0.25) + (3 \\times 0.10) + (4 \\times 0.20) + (5 \\times 0.29)
]<\/p>\n\n\n\n

[
E(X) = 0 + 0.15 + 0.50 + 0.30 + 0.80 + 1.45
]<\/p>\n\n\n\n

[
E(X) = 3.20
]<\/p>\n\n\n\n

\n\n\n\n

Explanation:<\/h3>\n\n\n\n

The missing probability was determined by ensuring the total probability equals 1, which is a fundamental rule in probability distributions. The probability that ( X=5 ) was calculated as 0.29.<\/p>\n\n\n\n

For ( P(X=2) ), we directly referenced the table.<\/p>\n\n\n\n

For ( P(X \\geq 3) ), we summed the probabilities of all values of ( X ) that are at least 3.<\/p>\n\n\n\n

The expected value, ( E(X) ), is essentially the weighted average of ( X ), considering the probabilities as weights. It provides an idea of the “center” of the distribution. In this case, ( E(X) = 3.20 ), meaning that, on average, the expected value of ( X ) is around 3.2.<\/p>\n\n\n\n

This approach to solving probability distribution questions ensures an understanding of fundamental probability concepts like probability summation, cumulative probability, and expected values.<\/p>\n","protected":false},"excerpt":{"rendered":"

find the missing probability in the table below, assume that X can only be 0 X P(X) 0 0.01 1 0.15 2 0.25 3 0.10 4 0.20 5 ??? a.)Given the rest of the table, what is P(X =5)? b) What is P(X=2)? c) What is P(X 3)? d) What is E(X)? The Correct Answer […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-187739","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/187739","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=187739"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/187739\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=187739"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=187739"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=187739"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}