roblems, how does the total number of counters change for the second pick?","back":"It stays the same (the counter is put back).","points":1},{"id":"4ae37d94-17b2-44c7-9253-7b9af78a9ac9","cardType":"basic","front":"If a bag has $x$ counters and one is taken without replacement, what is the new total for the second pick?","back":"$$x - 1$","points":1},{"id":"f0c188ab-b9c7-41f1-a531-4d1ecb2927b7","cardType":"basic","front":"A bag has 3 red and $x$ blue counters. What is the probability that the first pick is blue?","back":"$$\\frac{x}{x+3}$","points":1},{"id":"c317b769-cfec-4dab-9df6-713255556e27","cardType":"basic","front":"A bag has 3 red and $x$ blue counters. If the first pick was blue and not replaced, what is the probability the second pick is blue?","back":"$$\\frac{x-1}{x+2}$","points":2},{"id":"d4ced2e9-879f-44ee-83ba-8ad9d74da59d","cardType":"basic","front":"If the ratio of red to blue counters is $3:1$, how should you represent the counts algebraically using a multiplier $k$?","back":"

Red: $3k$
Blue: $k$

","points":2},{"id":"00276559-2272-4db2-ae04-289b21643f26","cardType":"basic","front":"If the ratio of red to blue counters is $3:1$, what is the algebraic expression for the total number of counters?","back":"$$4k$","points":1},{"id":"a6b0d8b6-0bb0-45ba-9be4-071102049835","cardType":"basic","front":"Why must you always use the positive square root when solving for numbers of counters or probabilities?","back":"The number of counters and probabilities cannot be negative.","points":1},{"id":"9bd18dac-031e-4580-b128-777629832fa5","cardType":"basic","front":"A quadratic for total counters $n$ gives $n = 21$ and $n = 4$. If there are 6 red counters in the bag, why is $n = 4$ rejected?","back":"The total number of counters cannot be less than the number of red counters already known to be inside.","points":2},{"id":"8521c11c-2c5d-4b95-995a-dddf012c8e18","cardType":"basic","front":"In a ratio of red:blue = $3:2$, what is the initial probability of picking a blue counter?","back":"$$\\frac{2k}{5k}$ (which simplifies to $\\frac{2}{5}$)","points":1},{"id":"688acf54-e68e-4542-859f-07ab264a03f2","cardType":"basic","front":"In a ratio of red:blue = $3:2$, if one blue counter is removed, what is the probability the second counter is blue?","back":"$$\\frac{2k-1}{5k-1}$","points":2},{"id":"d7f013ee-1418-422e-bfa7-99eeda6af6a7","cardType":"basic","front":"A bag has $n$ counters. 6 are red and the rest are blue. What is the algebraic expression for the number of blue counters?","back":"$$n - 6$","points":1},{"id":"6ba41956-20b3-42ef-b554-e751598b230b","cardType":"basic","front":"In a \"show that\" question involving a quadratic, what should be your first line of working?","back":"The probability equation (the product of two fractions equal to the given probability).","points":1},{"id":"e99f369c-e442-4ab0-a297-defd1ca750b5","cardType":"basic","front":"When solving $\\frac{x}{x+3} \\times \\frac{x-1}{x+2} = \\frac{5}{14}$, what is the standard method to remove the fractions?","back":"Cross-multiply the numerators and denominators.","points":1},{"id":"500cdb6d-686c-4eda-b288-f16cd4301251","cardType":"basic","front":"A bag has $y$ blue and 6 red counters. Without replacement, what is the probability of picking blue then red?","back":"$$\\frac{y}{y+6} \\times \\frac{6}{y+5}$","points":2},{"id":"1d0cd5cc-4efc-4f80-8607-4d5bbc77a7e5","cardType":"basic","front":"Why does the denominator decrease in \"without replacement\" probability even if a different colour is picked second?","back":"The total number of counters in the bag has decreased by 1.","points":1}]}],"examCountdown":{"examDate":"2027-05-14","paperLabel":"Paper 1"},"formulaUrl":"https://assets.mathsgenie.co.uk/board-resources/gcse-mat

Probability Equation Questions Flashcards

Probability Equation Questions Flashcards

Probability Equation Questions Flashcards

Probability Equation Questions Flashcards