i) Thaksh spun both the spinners, A and B in one of his turns.

Question

Answer the questions based on the given information.

Rubiya, Thaksh, Shanteri, and Lilly entered a spinning zone for a fun game, but there is a twist: they don't know which spinner will appear on their screens until it is their turn to play. They may encounter one of the following spinners, or perhaps even both

Different combinations of numbers will lead to exciting prizes. Below are some of the rewards they can win: 

♦ Get the number '5', from Spinner A and '8' from Spinner B, and you'll win a music player! 

♦ You win a photo frame if Spinner A lands on a value greater than that of Spinner B!

i) Thaksh spun both the spinners, A and B in one of his turns. 

What is the probability that Thaksh wins a music player in that turn? Show your steps. 

ii) Lilly spun spinner B in one of her turns. What is the probability that the number she got is even given that it is a multiple of 3? Show your steps.

iii) Rubiya spun both the spinners. What is the probability that she wins a photo frame? Show your work.

OR 

iii) As Shanteri steps up to the screen, the game administrator reveals that for her turn, the probability of seeing Spinner A on the screen is 65%, while that of Spinner B is 35%. 

What is the probability that Shanteri gets the number '2'? Show your steps.

Answer 1

(i) Finds the required probability as:

P(5 from spinner A) ∩ P(8 from spinner B)

\(=\frac{1}{4}\times \frac{1}{8}\)

\(=\frac{1}{32}\)

(ii) Uses the conditional probability and finds the required probability as follows:

P(Even / Multiple of 3)

= P(Even ∩ Multiple of 3) / P(Multiple of 3)

\(=\frac{\frac{1}{8}}{\frac{2}{8}}\)

\(=\frac{1}{2}\)

(iii) Finds the probability of getting 2 from spinner A and getting 1 from spinner B as:

\(P_1 =\frac{1}{2}\times \frac{1}{8}=\frac {1}{16}\)

Finds the probability of getting 5 from spinner A and getting either 1, 2, 3 or 4 from spinner B as:

\(P_2= {\frac{1}{4}}\times [\frac{1}{8}+\frac{1}{8}+\frac{1}{8}+\frac{1}{8}]\)

\(=\frac{1}{4} \times \frac{4}{8}\)

\(=\frac{1}{8}\)

Writes that P₁ and P₂ are mutually exclusive and hence, finds the probability that she wins a photo frame as:

\(P_1+P_2 =\frac{1}{16}+\frac{1}{8}\)

\(=\frac{3}{16}\)

OR

Uses the theorem of total probability and writes: 

P(getting 2) = [P(Spinner A) × P(Getting 2|Spinner A)] + [P(Spinner B) × P(Getting 2|Spinner B)]

Finds the required probability by substituting the required probability as:

\([\frac{65}{100}\times \frac{1}{2}]+[\frac{35}{100}\times \frac{1}{8}]\)

\(=\frac{59}{160}\)