Question

1. A spinner is spun and a card is randomly drawn from a deck of 15 cards. The spinner is divided into four equal parts. One part of the spinner is yellow. Three cards in the deck are spades.

What is the probability of the spinner landing on yellow and a spade being drawn from the deck of cards?

Enter your answer as a fraction in simplest form in the box.

Answer 1

`(1)/(20)`

Explanation:

Given : A spinner is spun and a card is randomly drawn from a deck of 15 cards. The spinner is divided into four equal parts. One part of the spinner is yellow. Three cards in the deck are spades.

To Find: What is the probability of the spinner landing on yellow and a spade being drawn from the deck of cards

Solution :

The spinner is divided into four equal parts.

One part of the spinner is yellow.

Probability of getting yellow on spinner :
`\frac{\text{favorable outcomes}}{\text{total outcomes}}`

Total outcomes = 4 (since spinner is divided into 4 parts)

Favorable outcome ={yellow}=1

So, Probability of getting yellow on spinner :
`(1)/(4)`

Now, a card is randomly drawn from a deck of 15 cards.

Three cards in the deck are spades.

Probability of getting spade:
`\frac{\text{favorable outcomes}}{\text{total outcomes}}`

Total outcomes = 15 (since deck is of 15 cards)

Favorable outcome ={spades}=3(since there are 3 spades in deck)

So, Probability of getting spade :

`(3)/(15) =(1)/(5)`

So, the probability of the spinner landing on yellow and a spade being drawn from the deck of cards :

`(1)/(4)*(1)/(5)`

`(1)/(20)`

Hence the probability of the spinner landing on yellow and a spade being drawn from the deck of cards is
`(1)/(20)`