確率

{"meta":{"subjectId":"math","grade":"中学2年","field":"確率","unit":"確率","level":"標準","drillId":"math-2g002a"},"cards":[{"id":"1","front":{"title":"等しい起こりやすさの結果を数える","text":"公平なサイコロの各目は同じ起こりやすさと考えます。これを「同様に確からしい」といいます。\n5以上の目は5、6の2通りで、全体は6通り。確率は$\\frac{2}{6}=\\frac{1}{3}$です。条件に合う結果数を分子、全結果数を分母にします。","visual":{"kind":"dataVisual","rows":[["出る目","1","2","3","4","5","6"]],"alt":"本文の条件を整理した表。"}},"back":{"title":"等しい起こりやすさの結果を数える","text":"公平なサイコロで4以上の目は{blank:1}通り、全体は{blank:2}通り。確率は{blank:3}です。","answers":["3","6","$\\frac{1}{2}$"],"visual":{"kind":"dataVisual","rows":[["出る目","1","2","3","4","5","6"]],"alt":"本文の条件を整理した表。"}}},{"id":"2","front":{"title":"硬貨二回の四つの結果から選ぶ","text":"公平な硬貨を独立に2回投げると、表表・表裏・裏表・裏裏は同様に確からしい4通りです。\nちょうど一回表が出るのは表裏・裏表の2通りなので$\\frac{2}{4}=\\frac{1}{2}$です。「表が0回・1回・2回」の三分類は同じ起こりやすさではありません。","visual":{"kind":"dataVisual","rows":[["1回目／2回目","表","裏"],["表","表表","表裏"],["裏","裏表","裏裏"]],"alt":"本文の条件を整理した表。"}},"back":{"title":"硬貨二回の四つの結果から選ぶ","text":"公平な硬貨を独立に2回投げ、両方表となるのは{blank:1}通り。全体は{blank:2}通り、確率は{blank:3}です。","answers":["1","4","$\\frac{1}{4}$"],"visual":{"kind":"dataVisual","rows":[["1回目／2回目","表","裏"],["表","表表","表裏"],["裏","裏表","裏裏"]],"alt":"本文の条件を整理した表。"}}},{"id":"3","front":{"title":"二つのサイコロは組で数える","text":"公平なサイコロA、Bを独立に投げると、順序を区別した36個の組は同様に確からしいと考えられます。\n和が3になるのは(1,2)、(2,1)の2組で、確率は$\\frac{2}{36}=\\frac{1}{18}$です。和の2〜12を11個の等しい結果として数えてはいけません。","visual":{"kind":"dataVisual","rows":[["A／B","1","2","3","4","5","6"],["1","2","3","4","5","6","7"],["2","3","4","5","6","7","8"],["3","4","5","6","7","8","9"],["4","5","6","7","8","9","10"],["5","6","7","8","9","10","11"],["6","7","8","9","10","11","12"]],"alt":"本文の条件を整理した表。"}},"back":{"title":"二つのサイコロは組で数える","text":"公平なA、Bのサイコロを独立に投げます。和が2の組は{blank:1}、該当する組は{blank:2}個、確率は{blank:3}です。","answers":["(1,1)","1","$\\frac{1}{36}$"],"visual":{"kind":"dataVisual","rows":[["A／B","1","2","3","4","5","6"],["1","2","3","4","5","6","7"],["2","3","4","5","6","7","8"],["3","4","5","6","7","8","9"],["4","5","6","7","8","9","10"],["5","6","7","8","9","10","11"],["6","7","8","9","10","11","12"]],"alt":"本文の条件を整理した表。"}}},{"id":"4","front":{"title":"起こらないことは0、必ずなら1","text":"サイコロの目は1から6なので、7が出る結果は0通り。確率は$\\frac{0}{6}=0$です。\n6以下は全6通りが当てはまり$\\frac{6}{6}=1$です。確率は0以上1以下で、大きいほど起こりやすいことを表します。","visual":{"kind":"dataVisual","rows":[["出る目","1","2","3","4","5","6"]],"alt":"本文の条件を整理した表。"}},"back":{"title":"起こらないことは0、必ずなら1","text":"公平なサイコロで0の目が出る該当数は{blank:1}、確率は{blank:2}。1以上の目が出る確率は{blank:3}です。","answers":["0","0","1"],"visual":{"kind":"dataVisual","rows":[["出る目","1","2","3","4","5","6"]],"alt":"本文の条件を整理した表。"}}}],"questions":[{"id":"1","type":"choice","label":"サイコロの確率","question":"公平なサイコロを1回投げます。偶数の目が出る確率を選びなさい。","choices":["$\\frac{1}{2}$","$\\frac{1}{4}$","$\\frac{2}{3}$","$\\frac{5}{6}$"],"hint":"1〜6のうち条件に合う目を数えます。","explanation":"当てはまる目は[2, 4, 6]の3通り。全6通りなので$\\frac{1}{2}$です。"},{"id":"2","type":"choice","label":"サイコロの確率","question":"公平なサイコロを1回投げます。奇数の目が出る確率を選びなさい。","choices":["$\\frac{1}{2}$","$\\frac{1}{4}$","$\\frac{2}{3}$","$\\frac{5}{6}$"],"hint":"1〜6のうち条件に合う目を数えます。","explanation":"当てはまる目は[1, 3, 5]の3通り。全6通りなので$\\frac{1}{2}$です。"},{"id":"3","type":"choice","label":"サイコロの確率","question":"公平なサイコロを1回投げます。3の倍数の目が出る確率を選びなさい。","choices":["$\\frac{1}{3}$","$\\frac{2}{3}$","$\\frac{1}{6}$","$\\frac{2}{5}$"],"hint":"1〜6のうち条件に合う目を数えます。","explanation":"当てはまる目は[3, 6]の2通り。全6通りなので$\\frac{1}{3}$です。"},{"id":"4","type":"choice","label":"サイコロの確率","question":"公平なサイコロを1回投げます。4以上の目が出る確率を選びなさい。","choices":["$\\frac{1}{2}$","$\\frac{1}{4}$","$\\frac{2}{3}$","$\\frac{5}{6}$"],"hint":"1〜6のうち条件に合う目を数えます。","explanation":"当てはまる目は[4, 5, 6]の3通り。全6通りなので$\\frac{1}{2}$です。"},{"id":"5","type":"choice","label":"サイコロの確率","question":"公平なサイコロを1回投げます。2以下の目が出る確率を選びなさい。","choices":["$\\frac{1}{3}$","$\\frac{2}{3}$","$\\frac{1}{6}$","$\\frac{2}{5}$"],"hint":"1〜6のうち条件に合う目を数えます。","explanation":"当てはまる目は[1, 2]の2通り。全6通りなので$\\frac{1}{3}$です。"},{"id":"6","type":"choice","label":"サイコロの確率","question":"公平なサイコロを1回投げます。5の目が出る確率を選びなさい。","choices":["$\\frac{1}{6}$","$\\frac{1}{2}$","$\\frac{2}{3}$","$\\frac{5}{6}$"],"hint":"1〜6のうち条件に合う目を数えます。","explanation":"当てはまる目は[5]の1通り。全6通りなので$\\frac{1}{6}$です。"},{"id":"7","type":"choice","label":"硬貨二回","question":"公平な硬貨を独立に2回投げます。ちょうど一回表となる確率を選びなさい。","choices":["$\\frac{1}{2}$","$\\frac{1}{3}$","$\\frac{1}{4}$","$\\frac{3}{4}$"],"hint":"四つの順序付き結果から数えます。","explanation":"全4通りのうち2通りなので$\\frac{1}{2}$です。","visual":{"kind":"dataVisual","rows":[["1回目／2回目","表","裏"],["表","表表","表裏"],["裏","裏表","裏裏"]],"alt":"本文の条件を整理した表。"}},{"id":"8","type":"choice","label":"硬貨二回","question":"公平な硬貨を独立に2回投げます。二回とも表となる確率を選びなさい。","choices":["$\\frac{1}{4}$","$\\frac{1}{2}$","$\\frac{1}{3}$","$\\frac{3}{4}$"],"hint":"四つの順序付き結果から数えます。","explanation":"全4通りのうち1通りなので$\\frac{1}{4}$です。","visual":{"kind":"dataVisual","rows":[["1回目／2回目","表","裏"],["表","表表","表裏"],["裏","裏表","裏裏"]],"alt":"本文の条件を整理した表。"}},{"id":"9","type":"choice","label":"硬貨二回","question":"公平な硬貨を独立に2回投げます。二回とも裏となる確率を選びなさい。","choices":["$\\frac{1}{4}$","$\\frac{1}{2}$","$\\frac{1}{3}$","$\\frac{3}{4}$"],"hint":"四つの順序付き結果から数えます。","explanation":"全4通りのうち1通りなので$\\frac{1}{4}$です。","visual":{"kind":"dataVisual","rows":[["1回目／2回目","表","裏"],["表","表表","表裏"],["裏","裏表","裏裏"]],"alt":"本文の条件を整理した表。"}},{"id":"10","type":"choice","label":"二つのサイコロ","question":"公平なサイコロA、Bを独立に投げます。和が4になる確率を選びなさい。","choices":["$\\frac{1}{12}$","$\\frac{1}{11}$","$\\frac{1}{4}$","$\\frac{1}{2}$"],"hint":"36個の(A,B)の組で条件に合うものを数えます。","explanation":"和が4になる組は3個。全36個なので$\\frac{1}{12}$です。"},{"id":"11","type":"choice","label":"二つのサイコロ","question":"公平なサイコロA、Bを独立に投げます。和が7になる確率を選びなさい。","choices":["$\\frac{1}{6}$","$\\frac{1}{11}$","$\\frac{1}{2}$","1"],"hint":"36個の(A,B)の組で条件に合うものを数えます。","explanation":"和が7になる組は6個。全36個なので$\\frac{1}{6}$です。"},{"id":"12","type":"choice","label":"二つのサイコロ","question":"公平なサイコロA、Bを独立に投げます。和が12になる確率を選びなさい。","choices":["$\\frac{1}{36}$","$\\frac{1}{11}$","$\\frac{1}{12}$","$\\frac{1}{6}$"],"hint":"36個の(A,B)の組で条件に合うものを数えます。","explanation":"和が12になる組は1個。全36個なので$\\frac{1}{36}$です。"},{"id":"13","type":"choice","label":"起こらない事象","question":"サイコロで8が出る確率を選びなさい。","choices":["0","1","$\\frac{1}{6}$","$\\frac{1}{8}$"],"hint":"目は1から6です。","explanation":"該当する結果がないので確率0です。"},{"id":"14","type":"choice","label":"必ず起こる事象","question":"サイコロで6以下が出る確率を選びなさい。","choices":["1","0","$\\frac{5}{6}$","$\\frac{1}{6}$"],"hint":"すべての目が条件に合います。","explanation":"6通り中6通りで確率1です。"},{"id":"15","type":"choice","label":"和の起こりやすさ","question":"二つの公平なサイコロの和2と和7について選びなさい。","choices":["和7の方が起こりやすい","和2の方が起こりやすい","和の値は全て同じ確率","和2も和7も起こらない"],"hint":"和2は1組、和7は6組です。","explanation":"同様に確からしいのは36個の組で、和の各値ではありません。"}]}