A few days ago
Anonymous

Can someone please explain how to do the following problem

“A coin is tossed and a card is drawn from a standard 52 deck of cards. What is the probability of tossing a heads on the coin and drawing a queen of hearts?”

A few days ago
Mitch

This scenario is known as conditional probability.

“The probability of a particular event occurring,

given that another event has occurred.”

Here’s an example:

Suppose you’re playing a board game and

you need to roll exactly two sixes to win…

What’s the probability that you win the game?

1/6 * 1/6 = 1/36 = 0.27777 or 2.7%

The same rule applies to your problem.

Probability of a fair coin landing on heads = 1/2

Probability of drawing a queen of hearts = 1/52

Probability that both will happen?

1/2 * 1/52 = 1/104 = .009615 (slightly less than 1%)

~ Mitch ~

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A few days ago
norcekri
Where are you stuck? You should be able to get the individual probabilities:

What is the probability of getting heads on a coin flip?

What is the probability of drawing the queen of hearts?

Now, you need to combine them. Are they independent events? In other words, does the coin flip affect what card you draw, or vice versa? If so, you need to take that dependence into account. If not, then you simply apply the probability formula for two independent events: multiply the individual probabilities.

For instance, if the probability of getting heads is 2/3, and the probability of drawing the queen of hearts is 1/12, you figure the joint probability as 2/3 * 1/12 = 1/18.

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