Question

If Mr.B has a stack of 6 cards numbered 1 through 6. He randomly chooses a card without replacing it the first card drawn, randomly chooses a second card. What is the probability that Mr.B would would pick two cards that are less than 4?

Answer 1

Answer: 1/5

1/5 = 0.20 = 20%

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Step-by-step explanation:

• event space = {1,2,3} = set of cards less than 4
• sample space = {1,2,3,4,5,6} = set of all possible outcomes

There are 3 items in the event space out of 6 items in the sample space. Divide the two values to get 3/6 = 1/2.

The probability of getting a card less than 4 is 1/2.

One of the cards in the event space is chosen and not put back.

The number of items in the event space is now 3-1 = 2.

The number of items in the sample space is now 6-1 = 5

We get 2/5 as the probability of getting another card that is smaller than 4.

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Quick recap:

• 1/2 = probability the first card is less than 4
• 2/5 = probability the second card is less than 4, if the first card is not put back (aka no replacement)

Multiply those two fractions:

(1/2)*(2/5) = (1*2)/(2*5) = 1/5 is the final answer as a fraction

1/5 = 0.20 in decimal form. It converts to 20%