Question

A fair five sided dice with sides 1-5 is tossed 3 times. Find the probability that at least two will be odd

Answer 1

@ganeshie8

Answer 2

@Hero @kropot72

Answer 3

whats the probability for getting an odd number in a single toss ?

Answer 4

3/5

Answer 5

good, you want to find probability for atleast two toss results being odd

Answer 6

that means you can have :
1) an odd number on exactly two tosses

or

2) an odd number on all three tosses

yes ?

Answer 7

yes

Answer 8

find the probability of each and add up

Answer 9

whats the probability of having `an odd number on exactly two tosses` ?

Answer 10

not sure can u show me

Answer 11

odd number on exactly two tosses means, one toss has to be even, yes ?

Answer 12

yes

Answer 13

probability for odd number on a toss = 3/5
probability for even number on a toss = 2/5

lets count how many ways we can have an `odd number on exactly two tosses` :

1) (3/5)(3/5)(2/5)

2) (3/5)(2/5)(3/5)

3) (2/5)(3/5)(3/5)

Answer 14

Easy! just notice that each way has probabilties for "two odd numbers" and "one even number"

Answer 15

the even number could appear on third, second, or first toss ^

Answer 16

so the probability for `having odd number on exactly two tosses` would be :

3*(3/5)(3/5)(2/5) = ?

Answer 17

36/125?

Answer 18

check again

Answer 19

oh 54/125

Answer 20

Yes! next work the probability for having an odd number on ALL 3 dice
(this should be easy)

Answer 21

81/125

Answer 22

try again, step by step

Answer 23

isn't it 3*(3/5 3/5 3/5)

Answer 24

probability for having an odd number on ALL 3 dice :

(3/5) * (3/5) * (3/5)

thats all

Answer 25

why is there no 3

Answer 26

you don't need to multiply by 3 here because you dont have any cases here

Answer 27

earlier you had cases because the "even number" can appear on either first or second or third dice

Answer 28

working probability for an odd number on ALL 3 dice is pretty straightforward

you know probability for odd number in a single toss = 3/5
since you want an odd number on ALL 3 dice, simply multiply the probabilties :

(3/5)(3/5)(3/5)

Answer 29

ok so is the final answer just the two added?

Answer 30

yes just add both the probabilities

Answer 31

so its 81/125
thanks again ganeshie

Answer 32

looks good !