Question

Suppose you are conducting an experiment consisting of rolling a twelve sided die, spinning a wheel with equal sections in the colors of the rainbow (red, orange, yellow, green, blue, indigo, violet), and flipping a coin.

What is the probability of getting a 5 or higher on the die roll, landing on a primary color on the wheel, and getting heads on the coin flip?

Answer 1

Let A be an event denoting appearance of 5 or higher number on a 12 sided die.

Let B be an event denoting land on a primary color on a wheel.

Let C be an event denoting head of a coin flip.

Now P(A)=P{5,6,7,8,9,10,11,12}= 8/12

As primary colors are red, green and blue, therefore P(B)=3/7

And P(C)=P(Head)=1/2

Also A,B,C are independent.

Therefore, Probability of getting 5 or higher number on the die, primary color on spin and flip of head=as A,B,C are independent

=8/12 * 3/7 * 1/2= 24/168= 0.142