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Sladkaya [172]
3 years ago
10

Lewis rolls a number cube and then chooses a card from a set of cards numbered 1 through 5. What is the probability that he will

roll an even number and choose an even numbered card?
Mathematics
1 answer:
IceJOKER [234]3 years ago
3 0

Answer:

\frac{1}{5}=0.2

Step-by-step explanation:

The general formula for a probability is:

P=\frac{FavorableEvent}{TotalEvents}

The favorable events for the cube to fall in a even number are:

2, 4, and 6 ⇒ <u>3 favorable events</u>

and in the cube the total events are:

1, 2, 3, 4, 5, 6 ⇒ <u>6 total events</u>

So the probability of rolling an even number in the cube is:

P=\frac{3}{6}\\\\\\ P=\frac{1}{2}

Now we do something similar to find the probability to choose a card with an even number.

The favorable events for an even numbered card are:

2, 4 ⇒<u> 2 favorable events</u>

and the total number of events in the cards is:

1, 2, 3, 4, 5 ⇒ <u>5 total events</u>

Thus, the probability to choose an even numbered card (according to the probability formula) is:

P=\frac{2}{5}

And finally, since we want both things to happen we must multiply both obtained probabilities:

  • the probability that he will roll an even number and choose an even numbered card:

P=\frac{1}{2}*\frac{2}{5} \\ \\P=\frac{2}{10} \\\\P=\frac{1}{5} =0.2

The probability is 1/5 which is equal to 0.2 or 20%

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