Question

1. a bag contains 4 cherry, 8 orange,

6 strawberry and 10 lemon gummy bears.
a gummy bear is chosen at random,
replaced, then another is chosen. find
each probability.
a) $p$(both lemon)
b) $p$(cherry, then orange)
c) $p$(strawberry, then lemon)

Explanation:

Step1: Calculate total gummy bears

Total = $4 + 8 + 6 + 10 = 28$

Step2: Solve part a (both lemon)

Probability of lemon: $\frac{10}{28} = \frac{5}{14}$. Multiply for two draws (with replacement):
$\frac{5}{14} \times \frac{5}{14} = \frac{25}{196}$

Step3: Solve part b (cherry then orange)

Probability of cherry: $\frac{4}{28} = \frac{1}{7}$. Probability of orange: $\frac{8}{28} = \frac{2}{7}$. Multiply:
$\frac{1}{7} \times \frac{2}{7} = \frac{2}{49}$

Step4: Solve part c (strawberry then lemon)

Probability of strawberry: $\frac{6}{28} = \frac{3}{14}$. Probability of lemon: $\frac{5}{14}$. Multiply:
$\frac{3}{14} \times \frac{5}{14} = \frac{15}{196}$

Answer:

a) $\frac{25}{196}$
b) $\frac{2}{49}$
c) $\frac{15}{196}$