Martin puts two bowls of fruit out for his friends. The bowl of grapes has 9 green grapes and 16 red grapes. The bowl of tangerines has 7 seeded and 3 seedless tangerines. Martin’s friend chooses a random grape and a random tangerine. What is the probability that she chooses a green grape and a seedless tangerine?<\/p>\n\n\n\n
The correct answer and explanation is:<\/strong><\/mark><\/p>\n\n\n\n To find the probability that Martin’s friend chooses a green grape<\/strong> and a seedless tangerine<\/strong>, we can use the multiplication rule for independent events<\/strong>, since choosing a grape and choosing a tangerine are separate, independent events.<\/p>\n\n\n\n There are:<\/p>\n\n\n\n So, the probability of choosing a green grape<\/strong> is: P(green grape)=925P(\\text{green grape}) = \\frac{9}{25}<\/p>\n\n\n\n There are:<\/p>\n\n\n\n So, the probability of choosing a seedless tangerine<\/strong> is: P(seedless tangerine)=310P(\\text{seedless tangerine}) = \\frac{3}{10}<\/p>\n\n\n\n Since both selections are independent, multiply the probabilities: P(green grape and seedless tangerine)=925\u00d7310=27250P(\\text{green grape and seedless tangerine}) = \\frac{9}{25} \\times \\frac{3}{10} = \\frac{27}{250}<\/p>\n\n\n\n To solve this probability problem, it\u2019s important to recognize that two separate events are occurring: one fruit is selected from the bowl of grapes, and one from the bowl of tangerines. Since these actions don\u2019t affect each other (the selection of a grape doesn’t impact the selection of a tangerine), we treat them as independent events<\/strong>. This means we can find the overall probability by multiplying<\/strong> the probabilities of each individual event.<\/p>\n\n\n\n First, we calculate the probability of selecting a green grape. The grape bowl contains 9 green grapes out of a total of 25 (9 green + 16 red). Therefore, the chance of picking a green grape is 9 out of 25, or 925\\frac{9}{25}.<\/p>\n\n\n\n Next, we find the probability of selecting a seedless tangerine. There are 3 seedless tangerines in a total of 10 (7 seeded + 3 seedless), so the probability of picking a seedless tangerine is 310\\frac{3}{10}.<\/p>\n\n\n\n To find the probability of both<\/strong> events happening together\u2014selecting a green grape and<\/strong> a seedless tangerine\u2014we multiply the two individual probabilities: 925\u00d7310=27250\\frac{9}{25} \\times \\frac{3}{10} = \\frac{27}{250}<\/p>\n\n\n\n This product represents the likelihood that both specific types of fruit are chosen at random. Fraction multiplication is straightforward: multiply the numerators (top numbers) together and multiply the denominators (bottom numbers) together. This gives us the final answer: 27250\\frac{27}{250}, which cannot be simplified further.<\/p>\n","protected":false},"excerpt":{"rendered":" Martin puts two bowls of fruit out for his friends. The bowl of grapes has 9 green grapes and 16 red grapes. The bowl of tangerines has 7 seeded and 3 seedless tangerines. Martin’s friend chooses a random grape and a random tangerine. What is the probability that she chooses a green grape and a […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-16352","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/16352","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=16352"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/16352\/revisions"}],"predecessor-version":[{"id":16353,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/16352\/revisions\/16353"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=16352"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=16352"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=16352"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\n\n\n\nStep 1: Total number of grapes<\/h3>\n\n\n\n
\n
Total grapes = 9 + 16 = 25<\/strong><\/li>\n<\/ul>\n\n\n\n
\n\n\n\nStep 2: Total number of tangerines<\/h3>\n\n\n\n
\n
Total tangerines = 7 + 3 = 10<\/strong><\/li>\n<\/ul>\n\n\n\n
\n\n\n\nStep 3: Multiply the two probabilities<\/h3>\n\n\n\n
\n\n\n\n\u2705 Final Answer: 27250\\frac{27}{250}<\/strong><\/h3>\n\n\n\n
\n\n\n\n\ud83d\udcd8 Explanation (Approx. 300 words)<\/h3>\n\n\n\n