Single events questions with answers

Questions

1. Question 1One outcome

   A bag contains $6$ red, $2$ blue and $4$ green balls. A ball is taken at random. Find the probability that it is green.

   Show the worked solution

   1. Step 1: P = favourable outcomes over total outcomes$\mathstrut \text{Total} = 6 + 2 + 4$$\text{Total} = 12$$\mathstrut P(\text{green}) = \dfrac{4}{12}$$P(\text{green}) = \dfrac{1}{3}$
2. Question 2“Not” and “or”

   A bag contains $3$ red, $5$ blue and $7$ green balls. A ball is taken at random. Find the probability that it is blue or green.

   Show the worked solution

   1. Step 1: Count the balls of either colour$\mathstrut \text{Favourable} = 5 + 7$$\text{Favourable} = 12$
   2. Step 2: Divide by the total and simplify$\mathstrut P = \dfrac{12}{15}$$P = \dfrac{4}{5}$
3. Question 3Numbered cards

   Cards numbered $1$ to $15$ are shuffled and one is drawn at random. Find the probability that the number is a prime number.

   Show the worked solution

   1. Step 1: List the numbers that are a prime number$2, 3, 5, 7, 11, 13$That is $6$ numbers out of $15$.
   2. Step 2: Divide and simplify$\mathstrut P = \dfrac{6}{15}$$P = \dfrac{2}{5}$
4. Question 4Find a missing number

   A bag contains $4$ red balls and some blue balls. The probability of taking a red ball is $\dfrac{1}{3}$. Find the number of blue balls in the bag.

   Show the worked solution

   1. Step 1: Let the total number of balls be n$\dfrac{4}{n} = \dfrac{1}{3}$$\mathstrut n = 4 \times \dfrac{3}{1}$$n = 12$
   2. Step 2: Blue = total − red$\mathstrut \text{Blue} = 12 - 4$$\text{Blue} = 8$
5. Question 5Balls added or taken out: find x

   A bag contains $3$ red balls and $9$ blue balls. $x$ more red balls are put into the bag. A ball is then taken at random. The probability that it is red is $\dfrac{2}{5}$. Find the value of $x$.

   Show the worked solution

   1. Step 1: The numbers of balls after the change, in terms of xRed balls: $3 + x$; all the balls: $12 + x$
   2. Step 2: P(red) = red balls ÷ all the balls: write the equation and cross-multiply$\dfrac{3 + x}{12 + x} = \dfrac{2}{5}$$5(3 + x) = 2(12 + x)$$15 + 5x = 24 + 2x$
   3. Step 3: Collect the x terms on one side and solve$3x = 9$$x = 3$
6. Question 6Two-way tables and groups

   The two-way table shows the visitors to a museum one morning. A visitor is chosen at random. Find the probability that the visitor is a member.

   	Members	Non-members	Total
   Adults	15	10	25
   Children	8	17	25
   Total	23	27	50

   Show the worked solution

   1. Step 1: Count the visitors who is a member$15 + 8 = 23$
   2. Step 2: Choose from everyone: the grand totalGrand total $= 50$
   3. Step 3: Probability = number that fit ÷ number to choose from$P = \dfrac{23}{50}$