{"id":6991,"date":"2021-10-22T14:28:52","date_gmt":"2021-10-22T08:58:52","guid":{"rendered":"https:\/\/mathemerize.com\/?p=6991"},"modified":"2021-10-25T01:51:22","modified_gmt":"2021-10-24T20:21:22","slug":"two-aeroplanes-i-and-ii-bomb-a-target-in-succession-the-probabilities-of-i-and-ii-scoring-a-hit-correctly-are-0-3-and-0-2-respectively-the-second-plane-will-bomb-only-if-the-first-misses-the-target","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/two-aeroplanes-i-and-ii-bomb-a-target-in-succession-the-probabilities-of-i-and-ii-scoring-a-hit-correctly-are-0-3-and-0-2-respectively-the-second-plane-will-bomb-only-if-the-first-misses-the-target\/","title":{"rendered":"Two aeroplanes I and II bomb a target in succession. The probabilities of I and II scoring a hit correctly are 0.3 and 0.2, respectively. The second plane will bomb only if the first misses the target. The probability that the target is hit by the second plane, is"},"content":{"rendered":"

Solution :<\/h2>\n

Let the events,<\/p>\n

A = Ist aeroplane hit the target<\/p>\n

B = 2nd aeroplane hit the target<\/p>\n

And their corresponding probabilities are<\/p>\n

P(A) = 0.3 and P(B) = 0.2<\/p>\n

\\(\\implies\\) P(A’) = 0.7 and P(B’) = 0.8<\/p>\n

\\(\\therefore\\)\u00a0 Required Probability = P(A’)P(B) + P(A’)P(B’)P(A’)P(B) + …….<\/p>\n

= (0.7)(0.2) + (0.7)(0.8)(0.7)(0.2) + …….<\/p>\n

= 0.14 [ 1 + 0.56 + \\((0.56)^2\\) + ….. ]<\/p>\n

= 0.14 \\(({1\\over {1 – 0.56}})\\)<\/p>\n

= \\(0.44\\over 0.44\\) = \\(7\\over 22\\) = 0.32<\/p>\n

\n

Similar Questions<\/h3>\n

At a telephone enquiry system, the number of phone calls regarding relevant enquiry follow. Poisson distribution with an average of 5 phone calls during 10 min time intervals. The probability that there is almost one phone call during a 10 min time period is<\/a><\/p>\n

A fair die is tossed eight times. The probability that a third six is observed on the eight throw, is<\/a><\/p>\n

If A and B are two mutually exclusive events, then<\/a><\/p>\n

A and B play a game, where each is asked to select a number from 1 to 25. If the two numbers match, both of them win a prize. The probability that they will not win a prize in a single trial is<\/a><\/p>\n

A die is thrown. Let A be the event that the number obtained is greater than 3. Let B be the event that the number obtained is less than 5. Then, \\(P(A \\cup B)\\) is<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Solution : Let the events, A = Ist aeroplane hit the target B = 2nd aeroplane hit the target And their corresponding probabilities are P(A) = 0.3 and P(B) = 0.2 \\(\\implies\\) P(A’) = 0.7 and P(B’) = 0.8 \\(\\therefore\\)\u00a0 Required Probability = P(A’)P(B) + P(A’)P(B’)P(A’)P(B) + ……. = (0.7)(0.2) + (0.7)(0.8)(0.7)(0.2) + ……. = …<\/p>\n

Two aeroplanes I and II bomb a target in succession. The probabilities of I and II scoring a hit correctly are 0.3 and 0.2, respectively. The second plane will bomb only if the first misses the target. The probability that the target is hit by the second plane, is<\/span> Read More »<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-global-header-display":"","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":"","theme-transparent-header-meta":"default","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":""},"categories":[43,44],"tags":[],"yoast_head":"\nTwo aeroplanes I and II bomb a target in succession. The probabilities of I and II scoring a hit correctly are 0.3 and 0.2, respectively. The second plane will bomb only if the first misses the target. The probability that the target is hit by the second plane, is<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathemerize.com\/two-aeroplanes-i-and-ii-bomb-a-target-in-succession-the-probabilities-of-i-and-ii-scoring-a-hit-correctly-are-0-3-and-0-2-respectively-the-second-plane-will-bomb-only-if-the-first-misses-the-target\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Two aeroplanes I and II bomb a target in succession. The probabilities of I and II scoring a hit correctly are 0.3 and 0.2, respectively. The second plane will bomb only if the first misses the target. The probability that the target is hit by the second plane, is\" \/>\n<meta property=\"og:description\" content=\"Solution : Let the events, A = Ist aeroplane hit the target B = 2nd aeroplane hit the target And their corresponding probabilities are P(A) = 0.3 and P(B) = 0.2 (implies) P(A’) = 0.7 and P(B’) = 0.8 (therefore)\u00a0 Required Probability = P(A’)P(B) + P(A’)P(B’)P(A’)P(B) + ……. = (0.7)(0.2) + (0.7)(0.8)(0.7)(0.2) + ……. = … Two aeroplanes I and II bomb a target in succession. The probabilities of I and II scoring a hit correctly are 0.3 and 0.2, respectively. The second plane will bomb only if the first misses the target. The probability that the target is hit by the second plane, is Read More »\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mathemerize.com\/two-aeroplanes-i-and-ii-bomb-a-target-in-succession-the-probabilities-of-i-and-ii-scoring-a-hit-correctly-are-0-3-and-0-2-respectively-the-second-plane-will-bomb-only-if-the-first-misses-the-target\/\" \/>\n<meta property=\"og:site_name\" content=\"Mathemerize\" \/>\n<meta property=\"article:published_time\" content=\"2021-10-22T08:58:52+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2021-10-24T20:21:22+00:00\" \/>\n<meta name=\"author\" content=\"mathemerize\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"mathemerize\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minute\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/mathemerize.com\/two-aeroplanes-i-and-ii-bomb-a-target-in-succession-the-probabilities-of-i-and-ii-scoring-a-hit-correctly-are-0-3-and-0-2-respectively-the-second-plane-will-bomb-only-if-the-first-misses-the-target\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/mathemerize.com\/two-aeroplanes-i-and-ii-bomb-a-target-in-succession-the-probabilities-of-i-and-ii-scoring-a-hit-correctly-are-0-3-and-0-2-respectively-the-second-plane-will-bomb-only-if-the-first-misses-the-target\/\"},\"author\":{\"name\":\"mathemerize\",\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df\"},\"headline\":\"Two aeroplanes I and II bomb a target in succession. 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