We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.

+0

# Probability worded problem

0
269
2 Hey there! I’m having trouble with questing 25c, any help would be appreciated.

Thankyou!

Jul 23, 2018

### Best Answer

#1
+1

Probability worded problem

Jane has three bags of lollies. In bag 1 there are three mints and three toffees,
in bag 2 there are three mints and two toffees and in bag 3 there are two mints and one toffee.
Jane selects a bag at random and then selects a lolly at random.

c the probability hat jane chose bag 1, given that she selects a mint.

$$\text{P(bag 1) = \dfrac13 } \\ \text{P(mint/bag 1) = \dfrac36} \\ \text{P(mint form bag 1) = P(bag 1)P(mint/bag 1) = \left(\dfrac13\right)\left(\dfrac36\right) = \dfrac16 }$$ Jul 23, 2018

### 2+0 Answers

#1
+1
Best Answer

Probability worded problem

Jane has three bags of lollies. In bag 1 there are three mints and three toffees,
in bag 2 there are three mints and two toffees and in bag 3 there are two mints and one toffee.
Jane selects a bag at random and then selects a lolly at random.

c the probability hat jane chose bag 1, given that she selects a mint.

$$\text{P(bag 1) = \dfrac13 } \\ \text{P(mint/bag 1) = \dfrac36} \\ \text{P(mint form bag 1) = P(bag 1)P(mint/bag 1) = \left(\dfrac13\right)\left(\dfrac36\right) = \dfrac16 }$$ heureka Jul 23, 2018
#2
+1

Solution:

$$\text {For these types of question, use the Total Probability Theorem/Formula.}\\ \mathbb{P}(B_1) =\mathbb{P}(B_2) =\mathbb{P}(B_3) = \dfrac{1}{3}\\ \text {Probability of mint from Bag} \tiny \text {#} \\ \mathbb{P}(M|B_1) = \dfrac{1}{2}\\ \mathbb{P}(M|B_2) = \dfrac{3}{5}\\ \mathbb{P}(M|B_3) = \dfrac{2}{3}\\ \;\\ \mathbb{P}(B_1|M) = \Big (\mathbb{P}(B_1) \cdot \mathbb{P}(M|B_1)\Big)\div \Big(\mathbb{P}(B_1) \mathbb{P}(M|B1) + \mathbb{P}(B_2)\mathbb{P}(M|B_2) +\mathbb{P} P(B_3) \mathbb{P}(M|B_3)\Big)$$

$$\text {The probability that Jane chose bag 1, given that she selects a mint is equal to the probability}\\ \text {Jane chose a mint from bag #1 divided by the probability that she selected a mint.}\\$$

$$\mathbb{P}(B_1|M) = \dfrac{\Big(\dfrac{1}{3} \cdot \dfrac{1}{2}\Big) }{\Big(\dfrac{1}{3} \cdot \dfrac{1}{2}\Big) + \Big(\dfrac{1}{3} \cdot \dfrac{3}{5}\Big) +\Big( \dfrac{1}{3} \cdot \dfrac{2}{3}\Big)}\\ \;\\ \hspace{1.8cm}=\dfrac {15}{53}\\ \;\\ \hspace{1.8cm} \approx 0.28301\\$$

GA

Jul 24, 2018
edited by GingerAle  Jul 24, 2018