Question

John rolls a number cube twice. What is the probability that the sum of the 2 rolls is less than 7, given that the first roll is a 1?
one over six

two over three

one over two

five over six

@vishweshshrimali5 can you help me?

Answer 1

Okay sum is to be less than 7 and first roll is 2, so what can we say about second roll ?

Answer 2

The second roll must be less than 5. Right ?

Answer 3

ugh... I guess. im not too sure

Answer 4

statistics isn't my strongest subject, sorry

Answer 5

Its okay

Answer 6

Lets think about this in a more mathematical way

Answer 7

Let the first roll = f

And let second roll = s

Now, it is given that sum (i.e. f+s) must be less than 7

Answer 8

2+3?

Answer 9

Why ?

Answer 10

because it's less than 7?

Answer 11

Yes you are correct about that but we have to find out the general solution. So, we have,

\[\large{f+s < 7}\]

Now, we were given this:

First roll is 1

So, f = 1

Thus,

\[\large{1+s < 7}\]

\[\large{\implies s < 6}\]

Answer 12

So, second roll must be less than 6. That means it can be 1,2,3,4,5

Answer 13

Oh, ok. I think I get it kinda

Answer 14

Good :)

Answer 15

Can you help me with 2 more problems if you don't mind?

Answer 16

What is the probability of drawing a diamond from a standard deck of cards on a second draw, given that a diamond was drawn on the first draw and not replaced?

Answer 17

twelve over fifty one

one over fifty two

one over fifty one

thirteen over fifty two

Answer 18

There are 13 diamond cards. Now you drew 1 diamond card so only 12 diamond cards are left in the pack and total number of cards left are 52 - 1 = 51 cards

Answer 19

where did 13 come from?

Answer 20

Actually that is a general information.

Total 52 cards with 13 cards of each pack - diamond, club, heart, spade

Answer 21

So 13 diamond cards :)

Answer 22

oh! well, I don't play cards so won't really know that lol but thank you

Answer 23

Its okay. Actually I too don't play cards \(\large{:)}\). Its just that I studied about them in high school

Answer 24

lol, one more question and you're free. thank you for your time :D

Answer 25

Sure :) And your welcome. It was not a bother at all

Answer 26

In a hospital ward, there are 10 nurses and 6 doctors. 4 of the nurses and 3 of the doctors are male. If a person is randomly selected from this group, what is the probability that the person is female or a doctor?


three over sixteen

six over sixteen

twelve over sixteen

nine over sixteen

Answer 27

Ahh this one is a little more tricky

Answer 28

There are two events in the question here.

1. Selected person is female. = E1

2. Selected person is doctor. = E2

Answer 29

Ok. What do I do with that?

Answer 30

Now we know this formula:

probability of happening of event E1 "OR" event E2 is:

\[\large{P(E_1 \cup E_2) = P(E_1) + P(E_2) - P(E_1 \cap E_2)}\]

Where:

\[\large{P(E_1 \cup E_2)}\] is probability of happening of event E1 or E2

\[\large{P(E_1)}\] is probability of happening of event E1

\[\large{P(E_2)}\] is probability of happening of event E2

\[\large{P(E_1 \cap E_2)}\] is probability of happening of event E1 and E2

Answer 31

Now in question you are asked about \(\large{P(E_1 \cup E_2)}\).

You can find out P(E1), P(E2) easily.