Question

A game is played by spinning a fair spinner with three equal sections
and rolling a fair six-sided dice. The rules of the game are shown
below.
Harry plays the game and scores 5.
If Millie then plays the game, what is the probability that her score will
be higher than Harry's score?
Give your answer as a fraction in its simplest form.
Pink
Blue
Yellow
Spinner outcome
Yellow
Blue
Pink
Game rules
Score
The number on the dice
Double the number on the dice
0 if the number on the dice is odd
7 if the number on the dice is even

Answer 1

Answer:

If Millie spins yellow, she must roll a 6.

If Millie spins blue, she must roll a 3, 4, 5, or 6.

If Millie spins pink, she must roll an even number.

P(Millie's score > 5) =

(1/3)(1/6) + (1/3)(2/3) + (1/3)(1/2) = 4/9

Answer 2

Answer:

$\displaystyle Probability=\frac{4}{9}$

Step-by-step explanation:

First create a Distribution Table to find all possible scores:

$\begin{array}{c|c c c}\cline{1-4} &Yellow&Blue&Pink\\\cline{1-4}1&1&2&0\\\cline{1-4}2&2&4&7\\\cline{1-4}3&3&6&0\\\cline{1-4}4&4&8&7\\\cline{1-4}5&5&10&0\\\cline{1-4}6&6&12&7\end{array}$

Given from the table:

• total number of scores (n(S)) = 3 × 6 = 18
• total number of scores that are higher than 5 (n(X)) = 8, where X = {(Yellow, 6), (Blue, 3), (Blue, 4),(Blue, 5), (Blue, 6), (Pink, 2), (Pink, 4), (Pink, 6)}

Probability of an Event:

$\boxed{Probability\ (P(X))=\frac{number\ of\ event\ (n(X))}{number\ of\ total\ events\ (n(S))} }$

$\displaystyle P(X)=\frac{8}{18}$

         $\displaystyle=\frac{4}{9}$