Question

a. Find the probability of randomly selecting a 6 AND then a Jack from a standard deck of cards with replacement.

b. Find the probability of randomly selecting a 6 AND then a Jack from a standard deck of cards without replacement.

c. Find the probability of rolling five 3’s in a row on a standard die.

d. Find the probability of rolling a 6 on a die AND then getting a head on a coin flip, in that order.

Answer 1

a)

Probability of selecting a 6 from a pack of cards =4/52 and
Probability of selecting a jack from a pack of cards =4/52 Since with replacment.
Therefore probability of randomly selecting a 6 AND then a Jack from a standard deck of cards =4/52*4/52=1/169

b)

Probability of selecting a 6 from a pack of cards =4/52 and
Probability of selecting second card as a jack from a pack of cards =4/51 Since with replacment.
Therefore probability of randomly selecting a 6 AND then a Jack from a standard deck of cards =4/52*4/51=0.00603

c)

Probability of rolling five 3's in a row =1/6*1/6*1/6*1/6*1/6=1/6⁵=0.0001286

d)

probability of rolling a 6 on a die AND then getting a head on a coin flip=1/6*1/2=1/12