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

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

Answer 2

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

1/5=0.2

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)=(6)/(10)`

Also,
`P(B|A)=(1)/(3)`

Hence, we are asked to find: P(A∩B)

We know that:

`P(B|A)=(P(A\bigcap B))/(P(A))\\\\\\(1)/(3)=(P(A\bigcap B))/((6)/(10))\\\\\\P(A\bigcap B)=(1)/(3)* (6)/(10)\\\\P(A\bigcap B)=(2)/(10)=(1)/(5)=0.2`

The probability is:

1/5=0.2