Question

A jar contains four coins: a nickel, a dime, a quarter, and a half-dollar. Three coins are randomly selected from the jar. (a) What is the probability that the selection will contain the half-dollar? (Enter an exact number as an integer, fraction, or decimal.)

Answer 1

The probability that the selection will contain the half-dollar is 3/4.

Explanation:

Consider the provided information.

A jar contains four coins: a nickel, a dime, a quarter, and a half-dollar.

Three coins are randomly selected from the jar.

Let N represents nickel, D for dime, Q for quarter and H for half dollar.

The number of possible choices are:

`E_1 = (NDQ),E_2 = (NDH), E_3 = (NQH), E_4 = (DQH)`

Now we need to find the probability that the selection will contain the half-dollar.

P(choose a half-dollar) =
`P(E_2)+P(E_3)+P(E_4)`

P(choose a half-dollar) =
`(1)/(4)+(1)/(4)+(1)/(4)`

P(choose a half-dollar) =
`(3)/(4)`

Hence, the probability that the selection will contain the half-dollar is 3/4.