Try it on paper first. A hint, the key idea and the worked solution are here when you need them.
A card is drawn at random from a standard pack of cards and hidden behind a screen. A friend peeks and says, "It is a face card." A face card is a jack, a queen or a king, and the pack has of them, three in each suit. Given this news, find the probability that the card is a king, the probability that it is a heart and the probability that it is red. Give decimals.
Once is given, the sample space is . So , which is when the outcomes are equally likely. Divide by the event after the bar.
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. The new sample space. The news leaves equally likely cards.
Step 2. A king. Four of the are kings. The probability is .
Step 3. A heart. Each suit has three face cards, so three of the are hearts. The probability is .
Step 4. Red. Hearts and diamonds are red, so of the are red. The probability is .
Answer: about , and .
Check. Without the news, the chance of a heart is too. Here the news about face cards happens to leave the chance of a heart unchanged.
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