{"id":6856,"date":"2021-10-21T21:08:41","date_gmt":"2021-10-21T15:38:41","guid":{"rendered":"https:\/\/mathemerize.com\/?p=6856"},"modified":"2021-10-25T02:02:24","modified_gmt":"2021-10-24T20:32:24","slug":"three-groups-a-b-c-are-contesting-for-positions-on-the-board-of-directors-of-a-company-the-probabilities-of-their-winning-are-0-5-0-3-0-2-respectively-if-the-group-a-wins-the-probability-of-int","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/three-groups-a-b-c-are-contesting-for-positions-on-the-board-of-directors-of-a-company-the-probabilities-of-their-winning-are-0-5-0-3-0-2-respectively-if-the-group-a-wins-the-probability-of-int\/","title":{"rendered":"Three groups A, B, C are contesting for positions on the board of directors of a company. The probabilities of their winning are 0.5, 0.3, 0.2 respectively. If the group A wins, the probability of introducing a new product is 0.7 and the corresponding probabilities for group B and C are 0.6 and 0.5 respectively. Find the probability that the new product will be introduced."},"content":{"rendered":"
Given P(A) = 0.5, P(B) = 0.3 and P(C) = 0.2<\/p>\n
\\(\\therefore\\) P(A) + P(B) + P(C) = 1<\/p>\n
then events A, B, C are exhaustive.<\/p>\n
If P(E) = Probability of introducing a new product, then as given<\/p>\n
P(E|A) = 0.7, P(E|B) = 0.6 and P(E|C) = 0.5<\/p>\n
= 0.5 \\(\\times\\) 0.7 + 0.3 \\(\\times\\) 0.6 + 0.2 \\(\\times\\) 0.5 = 0.35 + 0.18 + 0.10 = 0.63<\/p>\n
The probability of India winning a test match against the west indies is 1\/2 assuming independence from match to match. The probability that in a match series India\u2019s second win occurs at the third test is<\/a><\/p>\n A bag contains 4 red and 4 blue balls. Four balls are drawn one by one from the bag, then find the probability that the drawn balls are in alternate color.<\/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