Help, so You pick a card at random. Without putting the first card back, you pick a second card at random. There are 3 cards, a 5 a 6 and a 7 What is the probability of picking …

Question

asked Oct 17, 2022 19.5k views

1 Answer

Gilad Bar · Answer 1 · 2022-10-21T13:02:16+0000

Given:

There are 3 cards, a 5 a 6 and a 7.

You pick a card at random. Without putting the first card back, you pick a second card at random.

To find:

The probability of picking a 5 and then picking a 6.

Solution:

We have,

Total number of cards = 3

Number of card of 5 = 1

So, probability of getting a card of 5 is:

$P(5)=\frac{\text{Number of card of 5}}{\text{Total number of cards}}$

P(5)=(1)/(3)

After this selection, the remaining number of cards is 2. So, probability of getting a card of 6 in second draw is:

$P(6)=\frac{\text{Number of card of 6}}{\text{Total number of remaining cards}}$

P(6)=(1)/(2)

Now, the probability of picking a 5 and then picking a 6 is

$P(\text{5 then 6})=P(5)* P(6)$

$P(\text{5 then 6})=(1)/(3)* (1)/(2)$

$P(\text{5 then 6})=(1)/(6)$

Therefore, the probability of picking a 5 and then picking a 6 is
.