You decide to perform an experiment with a standard deck of 52 cards and a set of 6-sideddice. You start by randomly picking a card from the deck. If the card is a diamond, you roll2 dice and record the sum of the dice. Otherwise, you roll 1 die and record the value of thedie. If you wrote down a 5, what is the probability the card you drew was a diamond

Probability of diamond card selected when 5 is write down =  

Step-by-step explanation:

Given - You decide to perform an experiment with a standard deck of 52 cards and a set of 6-sided dice. You start by randomly picking a card from the deck. If the card is a diamond, you roll 2 dice and record the sum of the dice. Otherwise, you roll 1 die and record the value of the die.

To find - If you wrote down a 5, what is the probability the card you drew was a diamond ?

Proof -

Total Number of cards in a deck = 52

Total number of Diamond card in a deck = 13

Now,

P(diamond card) = =

P(not a diamond card) = 1 - =

Now,

Total outcomes when two dice are rolled  = 36

Total outcome of getting 5 when two dice are rolled = { (1,4), (2,3). (3,2), (4,1) }

So,

P(Sum 5 when two dice are rolled ) = =

P(Sum 5 when one dice is rolled ) =

Now,

P(sum 5 when diamond card is selected) = × =

P(sum 5 when diamond card is not selected = × =

Now,

Probability (Getting 5) = +   =

Now,

Probability of diamond card selected when 5 is write down =

                                                                                                   = × =

⇒Probability of diamond card selected when 5 is write down =