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Lesson Example Discussion Quiz: Class Homework

Step-3

Title: Probability

Grade: 1300-a Lesson: S4-L3

Explanation: Hello Students, time to practice and review the steps for the problem.

Lesson Steps

Step	Type	Explanation	Answer
1	Problem	If you randomly select two cards from a standard deck of 52 playing cards, what is the probability that both cards are aces?
2	Step	Probability of drawing the first ace: → There are 4 aces, and 52 total cards, → So the probability of drawing an ace first is \$4/52\$.
3	Step	Probability of drawing the second ace after one ace is removed: →After taking out the first ace, there are only 51 cards remaining. There are also only 3 aces left since you don’t draw the first one back in. →So, the probability of drawing another ace after taking out one already is \$3/51\$.
4	Step	Multiply the probabilities for independent events : \$("Probability of drawing 1st ace") times ("Probability of drawing 2nd ace")\$
5	Step	The probability of drawing two aces from a deck of cards is	\$4/52\$ × \$3/51\$
6	Step	Therefore probability of drawing two aces from a deck of cards is \$1/221\$.
7	Choice.A	This option is incorrect because \$1/74\$ is not equal and too far from the actual probability	\$1/74\$
8	Choice.B	This option is incorrect because probability of drawing 2 aces from the deck of cards is not equal to 74	74
9	Choice.C	This option is correct because \$1/221\$ is the actual probability of drawing two aces from a deck of cards	\$1/221\$
10	Choice.D	This option is incorrect because 221 is not equal to \$1/221\$ which is the actual probability of drawing 2 aces	221
11	Answer	Option	C
12	Sumup	Can you summarize what you’ve understood in the above steps?

Step

Type

Explanation

Answer

Problem

If you randomly select two cards from a standard deck of 52 playing cards, what is the probability that both cards are aces?

Step

Probability of drawing the first ace:
→ There are 4 aces, and 52 total cards,
→ So the probability of drawing an ace first is \$4/52\$.

Step

Probability of drawing the second ace after one ace is removed:
→After taking out the first ace, there are only 51 cards remaining. There are also only 3 aces left since you don’t draw the first one back in.
→So, the probability of drawing another ace after taking out one already is \$3/51\$.

Step

Multiply the probabilities for independent events : \$("Probability of drawing 1st ace") times ("Probability of drawing 2nd ace")\$

Step

The probability of drawing two aces from a deck of cards is

\$4/52\$ × \$3/51\$

Step

Therefore probability of drawing two aces from a deck of cards is \$1/221\$.

Choice.A

This option is incorrect because \$1/74\$ is not equal and too far from the actual probability

\$1/74\$

Choice.B

This option is incorrect because probability of drawing 2 aces from the deck of cards is not equal to 74

Choice.C

This option is correct because \$1/221\$ is the actual probability of drawing two aces from a deck of cards

\$1/221\$

Choice.D

This option is incorrect because 221 is not equal to \$1/221\$ which is the actual probability of drawing 2 aces

221

Answer

Option

Sumup

Can you summarize what you’ve understood in the above steps?