Question

In the drawing, six out of every 10 tickets are winning tickets. Of the winning tickets, one out of every three awards is a larger prize.
What is the probability that a ticket that is randomly chosen will award a larger prize?

Answer 1

Answer:

The probability that a ticket that is randomly chosen will award a larger prize is:

                        1/5=0.2

Step-by-step explanation:

Let A denote the event that the ticket is a winning ticket.

B denote the event that there is a larger prize.

A∩B denote the event that there is a larger prize on the winning ticket.

Let P denote the probability of an event.

Now according to the given information we have:

$P(A)=\dfrac{6}{10}$

Also, $P(B|A)=\dfrac{1}{3}$

Hence, we are asked to find: P(A∩B)

We know that:

$P(B|A)=\dfrac{P(A\bigcap B)}{P(A)}\\\\\\\dfrac{1}{3}=\dfrac{P(A\bigcap B)}{\dfrac{6}{10}}\\\\\\P(A\bigcap B)=\dfrac{1}{3}\times \dfrac{6}{10}\\\\P(A\bigcap B)=\dfrac{2}{10}=\dfrac{1}{5}=0.2$

            The probability is:

              1/5=0.2

Answer 2

Given that 6 out of 10 is a winning ticket then 1 out of 3 awards is a larger prize. So there are 2 larger prize in every 6 winning tickets drawn. So the probality of that a ticket will award a larger prize is 2/10 or 1/5